May 2019

Part III Prep

  1. Open the repo at https://github.com/dlab-berkeley/Geospatial-Fundamentals-in-R-with-sf

    • Download and unzip the zip file
    • Take note of where the folder is located
  2. Start RStudio and open a new script, or ./docs/03-raster_data.Rmd

  3. Set your working directory to the folder you unzipped

  4. Install the required libraries in RStudio, if you do not have them already

our_packages<- c("ggplot2", "sf", "units", "tmap", "raster")
for (i in our_packages) {
  if ( i %in% rownames(installed.packages()) == FALSE) {
    install.packages(i)
  }
}
  1. Open the slides, ./docs/03-raster_data.html, in your browser (or click the “Part 3 Slides” link the repo).

Part III Overview

Review basic raster concepts

Read in our previous spatial data and new raster data

Make some raster and combined raster-vector maps

Run some raster and raster-vector operations and analyses

R Spatial Libraries

Let’s load the libraries we will use

library(sf)     # simple features objects and methods
library(tmap)   # mapping spatial objects
library(raster) # reading in and operating on rasters

Set your working directory

Use setwd to set your working directory to the location of the tutorial files.

For example:

path = "/path/to/your/working_directory"
setwd(path)

Load some files from Parts I and II

SF Census Tracts

# Read in the 'sftracts_wpop' shapefile
SFtracts <- st_read("./data", "sftracts_wpop")
## Reading layer `sftracts_wpop' from data source `/home/drew/Desktop/stuff/berk/dlab/Geospatial-Fundamentals-in-R-with-sf/data' using driver `ESRI Shapefile'
## Simple feature collection with 195 features and 10 fields
## geometry type:  MULTIPOLYGON
## dimension:      XY
## bbox:           xmin: -122.5145 ymin: 37.70813 xmax: -122.328 ymax: 37.86334
## epsg (SRID):    4269
## proj4string:    +proj=longlat +datum=NAD83 +no_defs

SF Properties 2015

# Read in from CSV file
SFhomes <- read.csv('./data/sf_properties.csv', 
                    stringsAsFactors = FALSE)
# subset the data
SFhomes15 <- subset(SFhomes, as.numeric(SalesYear) == 2015)

# coerce to an `sf` object
SFhomes15_sf <- st_as_sf(SFhomes15, coords = c('lon', 'lat'),
                                                  crs = 4326)
#Reproject to the SFtracts projection
#NOTE: We're overwriting the previous SFhomes15_sf object here! This is
#fine to do if we want, but we should always beware.
SFhomes15_sf = st_transform(SFhomes15_sf, st_crs(SFtracts))

#check projection equality
st_crs(SFhomes15_sf) == st_crs(SFtracts)
## [1] TRUE

Section 1: Raster Data in R

Read in a Raster

Using the fabulous raster package

# Reading in and plotting raster files

#read in a Bay Area DEM (Digital Elevation Model)
#(from http://www.webgis.com/terr_pages/CA/dem1/sanfrancisco.html)
DEM = raster('./data/san_francisco-e.DEM')

Plot it

Make a quick map of the data to check it out

#plot it
plot(DEM)

Explore the Structure

To see a summary of the structure and content of a RasterLayer object, we can just enter the object’s name.

DEM
## class      : RasterLayer 
## dimensions : 1201, 1201, 1442401  (nrow, ncol, ncell)
## resolution : 0.0008333333, 0.0008333333  (x, y)
## extent     : -123.0004, -121.9996, 36.99958, 38.00042  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=NAD27 +no_defs +ellps=clrk66 +nadgrids=@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat 
## source     : /home/drew/Desktop/stuff/berk/dlab/Geospatial-Fundamentals-in-R-with-sf/data/san_francisco-e.DEM 
## names      : san_francisco.e 
## values     : -32768, 32767  (min, max)

You can view more detail in the RStudio Environment pane.

Explore the Structure

A raster should really just be a matrix of data, with metadata assiging it the correct location on the Earth’s surface, right?

In a raster object, the data and metadata will all be saved in their own ‘slots’, which are indexed by ‘@’ rather than ‘$’.

(‘Slots’ are components used to organize ‘S4’ objects. ‘S4’ is a data-type commonly used by third-party packages to define their own special data structures.)

Explore the Structure

Here’s some of the important metadata.

DEM@extent
## class      : Extent 
## xmin       : -123.0004 
## xmax       : -121.9996 
## ymin       : 36.99958 
## ymax       : 38.00042
DEM@crs
## CRS arguments:
##  +proj=longlat +datum=NAD27 +no_defs +ellps=clrk66
## +nadgrids=@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat
DEM@ncols
## [1] 1201

Explore the Structure

And notice that the DEM object is indeed an ‘S4’ object.

class(DEM)
## [1] "RasterLayer"
## attr(,"package")
## [1] "raster"
typeof(DEM)
## [1] "S4"

Explore the Structure

Note that a raster object’s structural organizaion and string-representation (the bit that is printed to the screen when you call the variable’s name) are fundamentally different from those of sf objects.

Explore the Structure

For example, a RasterLayer has information on the resolution.

DEM
## class      : RasterLayer 
## dimensions : 1201, 1201, 1442401  (nrow, ncol, ncell)
## resolution : 0.0008333333, 0.0008333333  (x, y)
## extent     : -123.0004, -121.9996, 36.99958, 38.00042  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=NAD27 +no_defs +ellps=clrk66 +nadgrids=@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat 
## source     : /home/drew/Desktop/stuff/berk/dlab/Geospatial-Fundamentals-in-R-with-sf/data/san_francisco-e.DEM 
## names      : san_francisco.e 
## values     : -32768, 32767  (min, max)

Explore the Structure

What does the resolution mean?

(DEM@extent@xmax - DEM@extent@xmin) / DEM@ncols
## [1] 0.0008333333
(DEM@extent@ymax - DEM@extent@ymin) / DEM@nrows
## [1] 0.0008333333
DEM
## class      : RasterLayer 
## dimensions : 1201, 1201, 1442401  (nrow, ncol, ncell)
## resolution : 0.0008333333, 0.0008333333  (x, y)
## extent     : -123.0004, -121.9996, 36.99958, 38.00042  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=NAD27 +no_defs +ellps=clrk66 +nadgrids=@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat 
## source     : /home/drew/Desktop/stuff/berk/dlab/Geospatial-Fundamentals-in-R-with-sf/data/san_francisco-e.DEM 
## names      : san_francisco.e 
## values     : -32768, 32767  (min, max)

It’s the cell-size! That is, the real-world distance of the x and y sides of each cell (i.e. pixel) in our RasterLayer, expressed in the distance units of the object (as determined by its projection).

Explore the Structure

As for our matrix of data, it should live somewhere inside the @data slot, right?

str(DEM@data)
## Formal class '.SingleLayerData' [package "raster"] with 13 slots
##   ..@ values    : logi(0) 
##   ..@ offset    : num 0
##   ..@ gain      : num 1
##   ..@ inmemory  : logi FALSE
##   ..@ fromdisk  : logi TRUE
##   ..@ isfactor  : logi FALSE
##   ..@ attributes: list()
##   ..@ haveminmax: logi TRUE
##   ..@ min       : num -32768
##   ..@ max       : num 32767
##   ..@ band      : int 1
##   ..@ unit      : chr ""
##   ..@ names     : chr "san_francisco.e"

Explore the Structure

There’s a bunch of stuff there. Let’s take a look at the @data@values slot…

DEM@data@values
## logical(0)

Explore the Structure

What happened there? How can our data be logical(0)? Where’s our data?

DEM@data@inmemory
## [1] FALSE
DEM@data@fromdisk
## [1] TRUE

It appears our data was not all read into memory. Instead, our RasterLayer object contains a pointer to where that data is held on disk (to save memory).

Explore the Structure

How do we see the values, then?

Well, we can still subset the values, using two-dimensional subsetting notation, just as we’d expect for a matrix.

DEM[10:15, 20:30]
##  [1] 39 41 39 41 38 36 27 21 15  9  4 24 25 23 26 23 23 17 12  8  5  2 10
## [24] 11  9 11  9 10  7  4  2  1  0  2  2  2  2  2  2  2  1  0  0  0  0  0
## [47]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

And we’ll get back a vector of the values from that subsetted matrix, unfolded.

Explore the Structure

We can even subset the entire thing, getting back all of the values.

DEM[,]
##     [1] 120 120 117 111 104  98  92  89  87  85  82  80  79  76  72  67  57
##    [18]  45  32  20  12   6   3   1   0   0   0   0   0   0   0   0   0   0
##    [35]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##    [52]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##    [69]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##    [86]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [103]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [120]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [137]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [154]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [171]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [188]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [205]   0   1   3  11  19  27  33  40  51  59  70  69  91 108 123 140 158
##   [222] 168 185 196 204 205 204 194 195 186 172 164 152 135 118 101  81  69
##   [239]  62  54  50  53  53  54  56  58  74  91 107 126 143 162 174 202 223
##   [256] 234 246 260 282 308 336 367 383 385 379 371 359 345 325 311 280 259
##   [273] 249 236 226 215 202 188 170 157 145 130 118 109 101  95  89  86  83
##   [290]  81  82  79  79  85  90  96  99 100 103 111 119 122 123 124 125 128
##   [307] 143 158 168 175 182 188 192 209 222 226 234 250 265 279 291 304 306
##   [324] 305 326 344 355 367 379 389 395 395 391 380 371 365 352 329 314 300
##   [341] 281 271 259 239 214 188 172 158 140 122 112 110 110 115 146 173 180
##   [358] 182 212 243 263 275 282 265 249 218 202 198 191 189 194 194 196 193
##   [375] 192 198 216 231 239 242 246 249 262 274 284 294 302 306 322 342 357
##   [392] 368 374 371 362 357 357 355 356 360 368 376 379 387 397 406 418 419
##   [409] 431 434 432 426 420 414 407 403 397 388 378 368 355 345 333 325 313
##   [426] 302 295 288 281 273 259 249 237 224 215 211 216 218 230 235 250 249
##   [443] 267 285 295 311 324 317 314 305 284 265 253 243 233 222 211 216 217
##   [460] 220 216 202 187 180 155 136 126 134 130 123 114 103  94  88  76  67
##   [477]  62  58  56  59  67  76  84  90  92  89  84  80  80  88  99 112 126
##   [494] 141 156 169 178 183 180 172 160 146 133 119 106  94  84  76  68  63
##   [511]  59  57  57  58  60  63  69  76  86  96 106 116 120 116 110 101  92
##   [528]  83  74  68  62  57  52  48  46  44  43  43  44  45  47  48  47  45
##   [545]  42  39  36  34  33  31  30  30  29  29  29  29  29  28  28  28  28
##   [562]  28  28  29  30  31  32  33  34  35  36  38  40  42  45  51  59  69
##   [579]  81  94 108 123 136 147 157 162 165 167 170 174 180 187 195 204 213
##   [596] 218 214 208 200 189 175 162 147 135 127 126 129 128 121 112 101  90
##   [613]  80  72  64  60  60  62  65  71  79  88  97 106 108 107 102  95  87
##   [630]  79  72  66  61  57  53  50  47  43  40  36  32  28  24  20  16  13
##   [647]   9   6   4   2   1   1   0   0   0   0   0   0   0   0   0   0   0
##   [664]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [681]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [698]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [715]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [732]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##   [749]   0   0   0   0   0   0   0   0   0   0   0   1   1   3   6   9  13
##   [766]  17  20  21  22  22  22  21  21  21  21  21  20  20  20  19  19  19
##   [783]  19  19  20  20  20  21  22  22  22  22  22  22  22  22  22  22  23
##   [800]  24  24  24  25  25  25  25  26  27  28  29  30  31  32  32  33  33
##   [817]  34  35  36  37  38  39  40  42  45  49  52  56  58  60  61  62  63
##   [834]  66  68  70  72  72  72  70  67  64  61  57  54  52  50  48  47  46
##   [851]  44  41  38  34  31  29  29  31  34  37  41  44  48  51  54  56  58
##   [868]  60  61  63  65  68  70  74  77  79  79  79  80  80  81  82  82  82
##   [885]  81  80  78  76  74  71  68  64  61  59  58  58  57  57  56  56  56
##   [902]  56  57  58  60  62  66  70  75  81  87  94 100 105 110 114 118 123
##   [919] 129 137 145 152 159 163 168 173 177 179 179 179 179 180 182 186 189
##   [936] 187 180 170 158 147 138 131 130 132 137 140 138 133 125 117 109 104
##   [953]  99  97  98 100 102 105 108 110 111 113 117 122 129 138 147 156 164
##   [970] 169 173 175 176 178 179 180 182 185 188 191 193 194 194 193 193 193
##   [987] 193 192 191 191 191 191 190 189 190 196 206 205 196 192 185 184 185
##  [1004] 189 193 196 199 200 200 199 207 198 179 159 142 127 116 109 108 109
##  [1021] 112 116 120 124 127 129 132 135 137 138 137 133 126 117 106  95  82
##  [1038]  71  61  53  48  45  43  42  42  43  45  48  51  56  60  62  63  62
##  [1055]  60  58  55  52  49  46  43  41  39  37  37  36  36  36  37  37  38
##  [1072]  38  38  38  37  37  36  36  36  36  36  35  35  36  38  41  44  47
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##  [1106]  36  34  32  29  27  24  22  20  19  18  17  17  17  17  18  19  20
##  [1123]  21  22  23  24  25  26  27  28  29  29  29  29  30  30  30  31  32
##  [1140]  33  33  33  33  33  33  33  34  34  34  33  33  33  34  34  35  35
##  [1157]  35  35  35  34  34  33  32  32  32  32  33  33  34  35  35  34  34
##  [1174]  34  34  34  35  36  38  39  40  40  39  38  38  37  36  35  35  34
##  [1191]  33  32  31  30  29  29  29  30  30  30  31 123 123 118 109 102  96
##  [1208]  89  85  83  82  81  80  79  76  72  67  57  45  32  19  11   6   3
##  [1225]   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
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##  [1378]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##  [1395]   0   0   0   0   0   0   0   0   0   0   0   0   0   1   7  16  23
##  [1412]  29  36  49  56  61  64  88 104 121 139 158 170 186 197 203 204 203
##  [1429] 193 186 180 169 159 149 134 117 100  81  69  61  52  47  44  47  52
##  [1446]  56  59  75  92 107 126 143 160 172 201 223 232 240 257 280 304 334
##  [1463] 366 382 385 381 373 360 345 325 311 280 259 254 247 235 222 208 195
##  [1480] 183 163 147 135 126 118 111 105  98  95  94  93  91  88  87  89  94
##  [1497]  99 101 101 103 111 119 123 125 124 123 122 141 157 168 176 183 190
##  [1514] 195 210 223 232 238 251 266 279 291 304 307 306 327 344 355 367 378
##  [1531] 388 393 393 391 382 372 367 353 329 314 300 289 277 266 254 221 191
##  [1548] 173 159 141 131 124 117 113 116 147 173 182 184 214 243 263 275 279
##  [1565] 264 249 218 202 191 186 186 186 187 190 187 184 195 214 230 233 232
##  [1582] 233 237 257 272 281 289 300 303 320 341 356 369 377 376 370 367 365
##  [1599] 362 362 366 372 378 385 392 400 409 419 425 433 439 437 432 428 422
##  [1616] 416 410 404 392 380 371 362 352 342 330 317 304 298 295 290 279 266
##  [1633] 253 242 234 227 222 223 227 234 239 252 251 268 285 297 314 326 318
##  [1650] 315 306 284 265 253 242 234 227 223 223 227 229 226 207 193 187 159
##  [1667] 141 130 134 139 131 120 109 102  95  81  71  64  59  55  58  65  72
##  [1684]  79  85  87  84  79  75  77  89 103 115 127 141 158 175 186 189 184
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##  [1718]  68  74  82  94 107 118 124 123 118 109 100  90  80  72  67  63  59
##  [1735]  55  53  51  50  49  49  49  49  48  47  45  43  41  40  38  36  35
##  [1752]  34  33  33  33  33  33  33  33  32  32  32  32  33  34  36  37  38
##  [1769]  38  39  41  43  45  47  50  53  57  66  77  90 106 124 141 156 167
##  [1786] 175 179 180 181 182 184 189 195 205 215 226 234 232 227 219 206 190
##  [1803] 174 156 145 138 145 150 145 136 124 111  97  86  77  72  70  69  71
##  [1820]  73  79  88  98 107 114 114 111 107  99  90  81  73  66  60  55  50
##  [1837]  45  42  39  36  33  29  25  22  19  15  12   9   6   4   2   1   0
##  [1854]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##  [1871]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##  [1888]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##  [1905]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##  [1922]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##  [1939]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
##  [1956]   0   0   0   0   0   0   2   4   7  10  13  16  18  20  20  20  20
##  [1973]  20  20  21  22  22  22  22  22  22  22  23  24  25  25  25  26  27
##  [1990]  28  29  30  30  30  30  30  30  30  30  31  32  33  33  34  34  34
##  [2007]  34  35  36  37  38  39  39  40  40  41  41  42  42  43  43  44  45
##  [2024]  46  48  50  52  55  58  60  62  63  63  65  68  72  75  77  77  76
##  [2041]  74  71  68  65  62  59  57  55  54  53  52  50  47  43  40  37  35
##  [2058]  35  36  39  43  46  50  52  55  57  58  60  61  62  65  68  72  77
##  [2075]  83  86  88  88  87  87  87  88  89  89  89  89  88  86  85  83  81
##  [2092]  76  71  68  66  64  62  60  58  56  54  54  54  55  57  60  63  66
##  [2109]  71  76  81  87  94 100 106 111 115 119 124 131 139 148 158 167 172
##  [2126] 177 180 184 186 186 188 187 186 189 193 195 192 185 173 159 147 139
##  [2143] 134 134 140 146 150 147 140 132 124 116 111 106 103 102 102 103 105
##  [2160] 106 107 108 111 115 122 131 141 150 157 163 167 170 172 173 174 175
##  [2177] 177 180 183 187 190 192 192 191 190 190 191 191 190 188 187 187 187
##  [2194] 188 188 192 206 230 240 229 218 208 202 199 200 200 200 201 202 204
##  [2211] 211 229 221 197 168 146 129 117 108 106 107 110 114 118 123 126 128
##  [2228] 132 137 139 140 139 136 130 121 111  99  86  75  65  57  53  51  50
##  [2245]  49  49  51  52  54  57  61  65  67  66  64  61  58  55  52  50  47
##  [2262]  44  42  40  39  39  39  39  39  39  39  38  38  38  38  38  38  38
##  [2279]  38  38  39  39  40  41  42  44  46  48  50  52  55  58  60  61  61
##  [2296]  61  62  63  65  65  63  61  58  53  49  45  41  39  36  34  31  27
##  [2313]  25  23  22  21  21  21  21  22  23  24  26  28  29  30  31  33  34
##  [2330]  36  37  38  38  38  38  38  38  39  40  41  42  42  42  42  42  42
##  [2347]  42  43  42  42  41  41  41  41  41  42  42  42  42  42  41  39  38
##  [2364]  37  36  35  35  35  37  38  39  39  38  37  36  36  36  37  38  38
##  [2381]  38  38  38  37  36  35  34  34  33  33  32  32  31  29  29  28  29
##  [2398]  29  29  30  30  31 127 127 119 113 106  99  92  88  86  84  81  79
##  [2415]  76  73  69  66  57  46  32  21  14   9   6   3   1   0   0   0   0
##  [2432]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
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##  [6376] 155 151 149 146 145 149 154 158 163 165 169 173 181 192 204 221 235
##  [6393] 252 269 286 323 363 393 411 398 385 363 340 319 306 304 310 323 350
##  [6410] 370 380 389 391 393 393 396 396 401 404 408 412 415 410 396 380 372
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##  [8008]  47  47  47  47  48  48  50  51  52  52  52  51  52  53  53  53  53
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##  [8314]  55  50  43  35  29  24  22  22  25  26  26  27  29  31  35  37  38
##  [8331]  39  41  43  45  48  50  50  50  48  49  49  50  50  51  53  55  56
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##  [8960]  46  46  47  47  47  47  47  47  48  48  48  50  51  52  53  54  55
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##  [9198]  43  44  44  44  44  44  44  45  47  48  48  48  48  48  48  48  49
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##  [9504]  60  60  60  60  60  60  60  60  60  60  59  56  50  42  34  27  23
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## [18225]   0   0   0   0   0   0   0   0   0   0   0   0   0   4  22  39  58
## [18242]  60  60  72  82  94 112 131 172 170 161 163 175 182 182 185 192 198
## [18259] 204 200 197 215 223 219 216 211 210 206 198 192 182 201 212 221 237
## [18276] 249 277 294 303 306 310 316 311 304 304 304 304 304 306 306 305 297
## [18293] 282 272 247 244 235 211 194 182 175 175 189 199 200 199 193 190 171
## [18310] 165 140 132 126 121 121 121 121 121 121 121 121 121 121 121 121 131
## [18327] 157 172 176 180 181 182 182 182 182 182 185 196 207 215 228 239 242
## [18344] 243 243 243 243 267 297 303 315 330 348 365 365 365 365 365 365 350
## [18361] 316 277 243 233 224 216 210 212 200 188 176 164 149 129 121 121 121
## [18378] 121 121 121 121 182 170 188 197 213 237 250 268 288 304 304 282 252
## [18395] 182 182 199 212 226 251 274 289 304 281 258 243 223 182 182 182 182
## [18412] 182 209 231 243 283 304 304 308 313 304 283 263 243 264 271 297 320
## [18429] 339 365 363 379 405 426 423 425 424 425 426 420 400 390 376 365 338
## [18446] 314 304 295 291 280 271 268 258 243 243 243 243 243 243 243 243 243
## [18463] 243 243 243 213 213 225 235 243 260 273 284 304 284 281 271 262 248
## [18480] 243 243 239 225 220 219 220 224 224 222 218 210 179 161 147 135 121
## [18497] 121 110  89  69  60  60  60  60  60  60  60  60  60  60  60  60  60
## [18514]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [18531]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  64  67
## [18548]  71  76  78  74  85 100 113 121 121 121  95  68  63  62  62  64  64
## [18565]  62  60  60  60  69  74  75  87 100  99  89  82  80  71  63  60  60
## [18582]  60  60  60  60  60  68  64  60  81 101 124 126 128 128 125 106  80
## [18599]  67  64  62  62  60 106 131 144 158 176 181 199 217 235 242 243 243
## [18616] 243 243 243 243 222 199 182 177 138 109  92  77  60  61  60  60  60
## [18633]  60  60  60  60  60  60  60  59  58  58  60  60  46  40  37  35  32
## [18650]  29  29  29  29  30  30  31  32  33  34  35  36  38  40  42  44  46
## [18667]  48  49  51  54  57  60  59  60  60  45  11   0   0   0   0   0   0
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## [18769]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   4
## [18786]   6   8  12  15  17  19  21  23  26  29  31  34  35  38  39  42  45
## [18803]  48  50  52  54  55  56  55  55  55  55  55  55  56  56  56  56  56
## [18820]  56  57  57  57  58  58  58  59  60  60  60  60  60  60  60  60  60
## [18837]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  61
## [18854]  62  62  62  62  62  62  61  60  60  60  77  82  84  83  78  72  66
## [18871]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  68  66
## [18888]  60  74  81  90  97 108 107 111 112 104 105 103 110 117 118 119 120
## [18905] 121 121 121 138 153 162 175 181 182 164 150 133 143 155 173 182 182
## [18922] 182 182 182 182 174 172 170 151 130 121 133 150 139 132 127 121 121
## [18939] 121 121 121 121 121 121 121 126 142 152 160 169 182 175 178 182 182
## [18956] 194 210 225 243 243 234 231 209 182 182 185 178 182 181 181 182 196
## [18973] 229 243 243 236 229 219 207 195 188 181 175 172 162 154 147 135 132
## [18990] 128 125 133 146 158 169 177 181 182 182 182 182 182 182 182 182 182
## [19007] 182 185 195 214 228 237 241 243 243 243 243 243 243 243 243 243 241
## [19024] 231 214 198 189 186 185 185 184 182 170 149 135 132 139 129 117 105
## [19041]  94  82  71  66  63  61  60  60  60  61  61  61  60  62  62  62  60
## [19058]  60  69  64  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [19075]  68  83 111 107  82  73  71  74  74  74  76  76  75  73  71  68  62
## [19092]  60  60  60  60  60  59  59  59  59  59  60  60  60  60  60  60  60
## [19109]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  59  51  42
## [19126]  33  24  22  24  27  29  29  29  30  32  34  38  39  40  40  43  44
## [19143]  47  50  51  51  51  48  49  51  51  51  51  54  56  56  56  56  56
## [19160]  57  57  57  53  52  52  52  52  52  52  52  52  52  52  49  48  48
## [19177]  45  44  44  44  44  44  47  48  49  46  45  45  44  44  43  43  42
## [19194]  41  40  39  38  37  36  35  35  34  33  32  31  30  30  30  28  26
## [19211]  25  25  26  28  34  37   0   0   0   0   0   0   0   7  16  20  20
## [19228]  15  10   7   6   5   3   2   1   1   0   0   0   0   0   0   0   0
## [19245]   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0
## [19262]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [19279]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
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## [19398]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [19415]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [19432]   0   0   0   0   0   0   0   0  11  33  60  60  60  67  72  77  91
## [19449] 103 121 144 138 140 153 168 182 187 202 215 226 224 229 238 238 235
## [19466] 233 233 235 243 243 243 243 243 243 243 251 277 304 300 307 312 319
## [19483] 330 339 322 304 304 304 302 304 304 304 304 304 304 275 250 243 227
## [19500] 208 182 182 182 208 224 231 243 225 217 202 188 182 165 149 137 124
## [19517] 121 121 121 121 121 121 121 121 121 121 131 141 155 171 178 180 181
## [19534] 182 182 182 182 188 195 203 212 229 243 242 243 243 243 243 266 288
## [19551] 304 312 334 354 365 365 365 365 365 365 365 319 284 243 243 240 236
## [19568] 234 243 227 209 195 182 174 161 131 121 121 121 121 121 126 170 182
## [19585] 192 204 218 239 256 272 295 302 303 304 268 213 182 203 218 230 257
## [19602] 297 301 302 304 280 268 255 247 213 182 182 182 199 228 243 304 301
## [19619] 313 324 334 324 311 294 283 281 289 297 309 331 349 365 392 421 424
## [19636] 425 425 425 425 426 415 398 385 369 360 345 334 322 314 309 298 296
## [19653] 295 287 265 251 243 243 243 240 229 217 208 198 198 192 189 182 199
## [19670] 213 224 236 247 242 253 263 263 261 259 255 243 243 236 221 222 224
## [19687] 234 243 243 243 243 243 212 177 164 152 141 130 123  99  74  60  60
## [19704]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [19721]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [19738]  60  60  60  60  60  60  60  60  60  60  60  62  63  63  62  60  76
## [19755]  83  87  99  99  78  64  62  63  64  66  68  68  66  60  75  85  92
## [19772] 100 111 121 121 109 100  98  91  78  67  60  60  60  60  60  60  60
## [19789]  60  60  60  60  92 121 122 122 121  91  60  64  61  60  61  60 106
## [19806] 136 150 164 182 182 191 206 215 218 234 243 243 243 243 243 237 211
## [19823] 198 182 143 118 103  89  78  66  60  60  60  60  60  60  60  60  60
## [19840]  59  58  56  56  56  54  43  37  35  33  31  28  28  29  29  29  30
## [19857]  30  32  32  33  34  36  38  41  44  46  48  51  53  57  58  60  60
## [19874]  60  60  60  43  16   0   0   0   0   0   0   0   0   0   0   0   0
## [19891]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [19908]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [19925]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [19942]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [19959]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [19976]   0   0   0   0   0   0   0   0   0   0   3   6   8  11  15  17  19
## [19993]  21  23  26  29  31  34  36  38  40  43  46  49  51  54  55  57  57
## [20010]  56  57  57  57  57  57  57  57  57  57  57  58  58  58  58  58  59
## [20027]  59  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [20044]  60  60  60  60  60  60  60  60  60  61  62  63  63  63  63  63  64
## [20061]  63  60  60  70  81  86  89  89  84  78  71  67  62  60  60  60  60
## [20078]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  71  76  88
## [20095]  91  95  92  89  89  85  95 106 111 116 120 121 121 121 133 142 149
## [20112] 157 157 150 121 121 128 121 143 168 182 182 182 182 182 182 182 181
## [20129] 182 182 156 160 159 182 166 160 157 152 135 125 121 121 121 121 121
## [20146] 121 121 126 137 141 147 145 158 167 174 179 182 190 204 215 232 240
## [20163] 243 234 213 206 204 202 196 193 187 182 204 238 242 243 242 239 232
## [20180] 221 210 202 196 189 184 174 168 164 156 145 138 134 143 154 164 172
## [20197] 178 180 182 182 182 182 182 182 182 182 182 183 183 187 199 218 231
## [20214] 239 242 243 243 243 243 244 246 245 244 240 227 205 197 192 193 193
## [20231] 196 189 184 174 160 141 149 165 160 141 126 115 106  89  74  70  64
## [20248]  62  61  62  64  64  63  64  73  72  74  75  84  97  84  69  60  60
## [20265]  60  60  60  60  60  60  60  60  60  60  60  66  88 121 118  83  73
## [20282]  73  77  77  79  83  85  83  80  78  74  66  60  60  60  62  62  61
## [20299]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [20316]  60  60  60  60  60  60  60  60  59  51  42  33  24  22  24  28  29
## [20333]  29  29  30  32  34  38  40  40  40  43  45  47  50  51  51  51  48
## [20350]  49  51  51  51  51  54  56  56  56  56  57  57  57  57  53  53  53
## [20367]  53  53  53  53  53  53  53  53  50  49  48  46  44  44  44  44  44
## [20384]  48  49  49  46  45  45  45  44  44  43  42  41  41  39  38  37  37
## [20401]  36  35  34  33  32  31  31  30  30  28  26  25  25  26  28  33  36
## [20418]   0   0   0   0   0   0   0   6  13  16  16  13  10   8   7   5   4
## [20435]   3   2   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20452]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20469]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20486]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20503]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20520]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
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## [20554]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20571]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20588]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20605]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20622]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [20639]   0   0   0   8  28  46  50  50  52  57  68  72  77 104 110 118 129
## [20656] 147 164 189 213 236 243 243 243 243 243 242 241 241 243 243 243 243
## [20673] 243 243 243 255 267 293 302 304 310 319 327 343 365 354 324 304 304
## [20690] 295 297 304 304 304 304 304 299 274 254 238 234 214 198 208 233 242
## [20707] 245 243 243 239 223 204 189 183 174 152 139 131 125 121 121 121 121
## [20724] 121 121 121 121 121 127 146 171 180 182 182 182 182 182 182 188 194
## [20741] 200 204 223 242 243 243 243 243 243 259 282 295 304 336 365 362 364
## [20758] 364 365 365 365 365 333 304 272 243 243 242 242 242 243 221 210 206
## [20775] 203 188 162 137 121 121 121 121 121 147 182 189 199 211 227 243 257
## [20792] 276 293 304 304 295 265 243 217 228 235 259 304 306 305 304 294 284
## [20809] 276 269 256 243 182 182 205 225 235 243 304 321 339 359 349 334 319
## [20826] 304 298 297 300 304 321 344 365 395 426 426 426 425 426 426 426 419
## [20843] 399 385 365 358 353 351 347 338 331 324 320 314 306 289 274 259 246
## [20860] 243 236 214 196 182 186 182 180 181 181 182 194 202 210 232 225 234
## [20877] 243 247 250 259 265 253 243 223 182 202 212 225 243 243 243 243 243
## [20894] 243 201 182 170 153 139 129 113  87  67  60  60  60  60  60  60  60
## [20911]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [20928]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [20945]  60  60  60  60  60  60  61  60  60  61  60  60  60  69  78  68  62
## [20962]  61  63  65  69  74  76  77  82  91 101 108 119 126 132 142 133 116
## [20979] 115 111  97  80  66  60  60  60  60  60  60  60  60  60  60  60  76
## [20996] 110 121 111  88  68  60  62  61  60  80 107 135 149 163 182 182 182
## [21013] 194 202 201 216 233 243 243 243 243 227 220 202 186 162 121 114 102
## [21030]  91  80  65  60  60  60  60  60  60  60  60  58  56  54  53  53  50
## [21047]  40  35  34  32  30  27  27  28  28  27  27  28  28  29  30  32  34
## [21064]  36  39  44  46  50  53  56  59  60  60  60  55  53  47  32  14   7
## [21081]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21098]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21115]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21132]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21149]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21166]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21183]   0   0   0   0   3   5   7  11  14  17  19  21  23  26  30  32  35
## [21200]  36  39  41  44  48  50  53  55  57  59  58  58  58  58  58  58  58
## [21217]  58  58  58  58  58  58  58  59  59  59  59  60  60  60  60  60  60
## [21234]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [21251]  60  60  60  61  62  64  65  65  65  66  67  67  69  70  77  88  93
## [21268]  97  99  93  87  79  73  67  62  60  60  60  60  60  60  60  60  60
## [21285]  60  60  60  60  60  60  60  60  60  60  71  75  77  77  75  72  67
## [21302]  82  97 105 112 121 121 121 121 124 129 133 136 134 125 124 123 122
## [21319] 121 135 162 181 178 182 182 182 182 182 182 182 182 170 170 178 182
## [21336] 182 177 182 168 151 131 122 121 121 121 121 121 121 121 121 121 121
## [21353] 121 140 156 164 172 182 182 182 185 204 222 243 237 240 240 235 243
## [21370] 227 223 210 210 220 243 243 242 243 243 240 232 224 217 211 202 193
## [21387] 185 180 178 172 160 151 146 153 162 170 175 179 181 182 182 182 182
## [21404] 182 182 182 183 186 188 186 185 199 217 230 238 242 243 243 243 245
## [21421] 251 253 249 246 243 232 219 207 203 206 209 206 195 188 181 173 167
## [21438] 174 178 179 170 159 140 131 117  98  83  71  68  65  72  76  74  70
## [21455]  77  87  92  94  89 103 121  99  78  60  60  60  60  60  60  60  60
## [21472]  60  60  60  60  60  60  60 105  94  81  74  75  80  83  89  97 103
## [21489]  96  92  88  81  71  68  65  67  66  65  62  60  60  60  60  60  60
## [21506]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [21523]  60  60  57  50  42  33  25  22  24  28  30  30  30  31  33  35  39
## [21540]  40  40  40  43  45  47  50  51  51  51  48  50  51  51  51  51  54
## [21557]  56  56  56  57  57  57  57  57  54  53  53  53  53  53  53  53  53
## [21574]  53  53  50  49  49  46  45  45  45  45  45  48  49  49  47  46  46
## [21591]  46  45  44  43  42  42  41  40  39  38  37  36  35  34  33  32  32
## [21608]  31  31  28  28  28  29  29  30  31  33  35   0   0   0   0   0   0
## [21625]   0   4  10  12  13  11   9   8   7   5   4   3   2   1   0   0   0
## [21642]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21659]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21676]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
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## [21710]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21727]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21744]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
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## [21795]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21812]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [21829]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  15
## [21846]  21  20  28  39  44  48  54  60  78 100 115 121 141 175 206 222 235
## [21863] 242 243 243 243 243 243 243 243 243 243 243 243 243 243 257 269 293
## [21880] 304 304 309 317 326 343 358 365 344 320 304 285 280 295 304 304 304
## [21897] 304 304 304 284 271 253 243 235 238 239 250 249 248 245 244 243 214
## [21914] 191 182 168 163 151 145 138 129 121 121 121 121 121 121 121 121 121
## [21931] 134 182 180 182 182 182 182 182 182 182 184 186 182 203 234 239 240
## [21948] 241 242 243 246 272 290 304 327 344 361 364 364 365 365 365 365 349
## [21965] 316 297 276 258 258 261 252 243 238 232 234 233 218 182 159 133 121
## [21982] 121 121 121 129 148 171 187 198 215 233 243 261 291 304 304 304 294
## [21999] 274 261 259 258 278 304 310 315 313 308 299 295 295 280 265 252 213
## [22016] 216 227 234 241 274 324 358 363 364 357 342 327 312 303 302 304 310
## [22033] 338 365 389 421 426 426 426 426 426 427 424 410 397 388 373 364 367
## [22050] 365 359 356 345 343 327 313 305 297 269 254 246 240 214 182 184 183
## [22067] 181 178 176 172 178 182 185 187 185 194 212 233 243 245 264 278 263
## [22084] 250 243 182 182 196 212 229 243 241 243 243 243 208 188 182 158 143
## [22101] 132 123 107  79  68  60  60  60  60  60  60  60  60  60  60  60  60
## [22118]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [22135]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [22152]  63  60  60  60  60  60  60  60  60  62  60  60  64  67  73  80  86
## [22169]  91  97 110 121 121 121 141 156 182 182 152 151 182 121  96  82  71
## [22186]  60  60  60  60  60  60  60  60  60  60  72  83  87  92  76  60  63
## [22203]  61  61  60  75 109 130 142 151 160 167 165 177 184 182 192 216 243
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## [43487]  29  37  47  54  58  59  60  90 121 128 139 147 155 163 169 175 181
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## [44031]  54  55  56  57  58  59  60  60  60  60  60  60  60  60  60  60  60
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## [44099]  96 107 111 115 119 121 121 121 121 121 121 121 121 121 153 170 179
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## [45017]  28  23  16  14  13  15  15  16  18  19  20  21  23  25  22  21  18
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## [45935] 376 387 402 426 405 365 341 320 304 262 243 243 228 205 185 175 160
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## [45969] 149 165 175 182 182 182 182 182 182 183 182 207 219 230 240 243 243
## [45986] 251 256 259 269 281 295 304 316 325 334 348 359 363 379 407 420 426
## [46003] 426 426 426 426 416 396 365 331 313 298 296 292 278 267 248 234 208
## [46020] 190 176 158 153 152 152 145 130 121 121 121 132 152 172 188 200 214
## [46037] 231 238 254 268 273 278 278 269 265 261 255 248 198 186 183 190 202
## [46054] 214 232 254 274 294 315 330 334 330 316 314 317 335 351 375 410 411
## [46071] 394 375 366 363 379 377 370 369 367 366 366 357 332 318 308 298 286
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## [46173]  60  60  60  67  74  78  84  92 110 121 121 121 121 120 121  94  81
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## [46734]  60  60  60  60  60  60  60  60  60  60  60  60  60  53  48  40  31
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## [46768]  53  53  53  51  53  53  53  53  53  56  57  57  57  57  57  57  57
## [46785]  56  56  56  56  56  56  56  56  56  56  56  56  56  56  56  55  55
## [46802]  55  55  55  56  57  57  57  57  57  57  56  56  55  54  54  53  52
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## [47618]  23  25  27  29  31  33  36  38  39  41  43  44  46  48  49  50  51
## [47635]  53  54  55  56  56  57  57  58  59  59  59  59  59  59  59  60  60
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## [47703]  95 102 110 118 121 121 121 121 121 133 150 172 178 181 192 203 218
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## [47958]  38  40  43  44  45  45  45  48  49  51  52  53  53  52  51  53  53
## [47975]  53  53  53  56  57  57  57  57  57  57  57  57  56  56  56  56  56
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## [48009]  57  57  58  58  57  56  56  55  55  54  53  52  52  51  50  49  49
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## [48825]  36  38  39  41  42  44  46  47  49  49  50  51  53  54  55  55  56
## [48842]  56  57  58  58  58  58  59  59  59  59  60  60  60  60  60  60  60
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## [48944]  92  91  89  89  87  87  88  87  88  92  95 101 110 118 117 119 120
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## [49165]  45  48  49  52  53  53  53  51  52  53  53  53  53  53  56  57  57
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## [50032]  45  46  47  49  49  50  52  53  53  54  55  56  56  57  58  58  58
## [50049]  58  59  59  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [50066]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [50083]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [50100]  60  60  67  72  78  85  92  99 105 111 115 119 121 121 121 128 131
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## [50151]  97  98 100 103 106 113 121 122 121 131 136 138 127 121 121 136 134
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## [50338]  65  64  62  60  60  60  60  60  60  60  60  60  54  51  41  31  30
## [50355]  37  38  38  38  38  39  41  44  45  45  45  45  48  49  52  53  53
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## [50729] 298 308 308 315 323 331 343 354 360 365 365 365 365 365 365 365 365
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## [50984]  68  89  98 121 121 121 121 121 101  82  60  60  60  60  60  60  60
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## [51222]  25  27  29  31  33  36  37  39  40  41  42  44  46  46  47  48  49
## [51239]  51  52  53  53  54  55  55  56  57  57  58  58  58  59  59  60  60
## [51256]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [51273]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [51290]  60  60  60  60  60  60  60  60  60  60  60  60  60  65  69  72  78
## [51307]  85  92  99 106 113 119 121 121 121 121 121 135 164 178 182 182 182
## [51324] 182 197 198 192 182 151 121 117 121 121 121 122 120 121 121 121 121
## [51341] 121 121 121 110 107 105 105 104 104 103 104 106 107 108 110 113 119
## [51358] 128 133 141 150 158 163 167 142 149 160 169 163 166 165 151 145 140
## [51375] 129 121 135 133 121 131 145 156 171 158 131 121 121 121 121 121 121
## [51392] 121 121 121 121 121 121 136 147 142 142 121 123 121 131 142 151 162
## [51409] 168 175 179 181 182 182 182 182 182 182 182 222 243 239 274 304 304
## [51426] 304 262 243 243 243 243 243 243 243 243 243 243 243 243 252 274 291
## [51443] 302 304 304 304 304 311 307 304 273 243 208 190 182 172 165 164 159
## [51460] 140 121 121 131 141 135 126 123 122 121 121 121 121 121 121 121 121
## [51477] 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121
## [51494] 121 121 121 121 121 121 121 121 121 121 121 121 121 128 129 129 122
## [51511] 121 121 121 121 121 121 121 121 121 121 110  95  77  60  62  60  61
## [51528]  60  60  81 103 121 111  98  86  76  71  69  66  64  62  60  60  60
## [51545]  60  60  60  60  60  60  55  52  41  32  30  37  38  38  38  38  39
## [51562]  42  44  45  45  45  45  48  49  52  53  53  53  52  52  53  53  53
## [51579]  53  53  56  57  57  57  57  57  57  57  57  57  57  57  57  57  57
## [51596]  57  57  57  57  57  57  57  57  57  57  57  57  57  58  58  58  59
## [51613]  59  59  59  59  58  58  57  56  55  54  54  53  53  52  51  50  49
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## [51902]  81  94 106 112 118 121 148 175 180 182 150 121 130 122 121 155 182
## [51919] 206 219 230 243 258 258 253 243 243 243 264 278 284 297 304 314 324
## [51936] 338 351 359 365 365 365 365 365 365 365 365 365 365 365 341 323 304
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## [51987] 182 188 191 191 189 182 191 200 203 214 226 236 243 256 284 304 316
## [52004] 330 341 351 365 371 382 396 409 426 426 426 430 439 448 445 436 426
## [52021] 402 381 365 365 304 298 300 314 312 304 283 263 243 219 195 182 155
## [52038] 121 121 121 137 158 182 182 182 182 181 180 181 181 182 182 182 182
## [52055] 182 182 200 208 214 236 243 232 232 243 243 265 275 298 312 327 338
## [52072] 346 360 374 374 371 367 365 365 358 322 312 307 305 304 295 294 297
## [52089] 302 305 305 305 302 292 288 284 283 278 266 256 250 244 243 243 243
## [52106] 243 243 243 243 243 243 243 236 230 225 220 216 206 192 182 182 182
## [52123] 178 172 175 143 128 121 133 138 135 128 122 122 121 123 131 141 161
## [52140] 182 199 224 243 261 290 304 296 282 268 249 233 194 161 140 121 105
## [52157]  90  68  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [52174]  60  60  60  60  60  60  60  60  60  60  60  69  77  83  93 112 121
## [52191] 121 121 121 101  88  73  60  60  60  60  60  60  60  60  60  60  60
## [52208]  60  60  60  60  56  53  49  46  43  39  35  32  29  25  22  19  16
## [52225]  14  12  10   7   5   1   0   0   0   2   2   2   1   2   2   2   2
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## [52412]   0   2   5   8  10  12  14  16  18  21  23  25  27  29  30  33  35
## [52429]  37  38  39  41  42  43  45  46  46  47  48  49  51  52  53  53  54
## [52446]  54  56  56  57  57  58  58  59  59  60  60  60  60  60  60  60  60
## [52463]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [52480]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [52497]  60  60  60  60  60  60  60  62  63  64  70  78  86  93 101 111 119
## [52514] 121 121 121 121 121 134 158 182 182 182 182 181 185 189 188 182 151
## [52531] 121 111 121 121 121 121 117 118 119 120 120 121 121 121 116 113 112
## [52548] 112 111 112 111 111 112 113 114 116 118 120 135 146 157 170 182 182
## [52565] 181 182 176 182 180 182 182 182 171 164 164 158 161 163 182 163 155
## [52582] 165 182 181 183 161 148 121 131 121 121 121 121 121 121 121 121 121
## [52599] 121 124 126 122 123 122 122 121 131 140 154 162 171 178 180 182 182
## [52616] 182 182 182 182 187 201 212 226 240 274 284 269 257 250 245 243 243
## [52633] 243 243 243 243 243 243 243 243 256 276 299 303 303 304 304 294 288
## [52650] 301 304 270 243 202 182 186 181 178 182 182 161 148 121 149 154 144
## [52667] 128 124 122 121 121 121 121 121 121 121 121 121 121 121 121 121 121
## [52684] 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121
## [52701] 121 121 121 121 121 121 121 121 122 123 121 118 117 118 121 121 121
## [52718] 121 121 121 121 114  98  80  70  60  60  60  60  60  60  80  88  93
## [52735]  92  85  77  72  69  66  64  62  60  60  60  60  60  60  60  60  60
## [52752]  55  53  42  29  35  38  39  39  39  38  40  42  44  45  46  46  46
## [52769]  48  49  52  53  53  53  52  52  53  53  53  53  53  56  57  57  57
## [52786]  57  57  58  57  57  57  57  57  57  57  57  57  57  57  57  57  57
## [52803]  57  57  57  57  57  57  58  58  59  59  59  59  60  60  60  59  58
## [52820]  58  56  56  55  54  53  53  52  51  50  49  49  48  47  46  45  45
## [52837]  44  43  42  41  42  43  44  48   0   0   0   0   0   0   0   0   0
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## [53092]   0   0   0   0   0   0   7  27  43  56  64  73  86 100 108 115 121
## [53109] 151 178 182 169 145 121 121 123 135 172 183 199 208 216 223 239 246
## [53126] 238 241 242 243 250 256 256 275 297 307 318 334 349 357 364 365 365
## [53143] 365 364 364 365 365 365 365 365 365 354 328 312 301 299 305 294 274
## [53160] 254 243 218 184 160 142 127 121 121 121 121 121 121 126 132 137 144
## [53177] 152 156 161 167 176 182 182 182 182 182 183 182 183 184 185 185 182
## [53194] 182 187 188 199 215 228 239 243 281 304 311 319 326 333 335 347 360
## [53211] 373 377 397 416 426 434 449 466 465 455 441 425 415 413 391 374 335
## [53228] 329 340 337 323 309 294 263 236 209 192 182 151 130 121 121 140 154
## [53245] 165 172 175 177 179 181 181 182 182 182 182 213 219 219 226 231 248
## [53262] 252 243 243 260 280 280 298 318 334 350 365 365 377 391 382 373 365
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## [53296] 304 304 304 292 278 264 255 243 243 243 243 243 243 243 243 243 243
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## [53330] 150 146 140 129 122 121 121 125 132 140 158 178 182 221 236 243 276
## [53347] 280 277 265 254 243 209 179 158 140 121 104  87  67  60  60  60  60
## [53364]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [53381]  60  60  60  60  60  60  62  61  69  88 101 118 121 121 121 113 110
## [53398]  80  68  60  64  60  60  60  60  60  60  60  60  60  60  60  57  53
## [53415]  50  47  45  41  38  35  32  29  26  23  19  17  16  14  12   9   5
## [53432]   2   2   5   5   5   5   4   4   4   4   3   3   2   1   0   0   0
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## [53534]   6  10  15  14   6   0   0   0   0   0   0   0   0   0   0   0   0
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## [53602]   0   0   0   0   0   0   0   0   0   0   0   0   2   5   8  10  12
## [53619]  14  16  18  21  23  25  27  29  30  33  35  37  38  39  40  41  42
## [53636]  44  44  45  46  47  48  50  51  52  53  53  54  55  56  56  57  57
## [53653]  58  59  59  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [53670]  60  60  60  60  61  60  60  60  60  60  60  60  60  60  60  60  60
## [53687]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [53704]  60  60  60  60  60  72  81  89  98 112 121 121 121 121 121 121 136
## [53721] 147 154 162 166 165 178 182 183 183 169 147 121  83  94 112 121 113
## [53738] 111 115 117 119 120 120 120 121 120 119 118 119 118 119 117 117 117
## [53755] 118 120 120 121 124 138 151 164 177 181 182 182 182 182 186 192 196
## [53772] 199 192 186 180 187 188 188 188 188 185 178 176 182 186 183 182 182
## [53789] 182 152 145 121 121 121 121 121 121 121 121 121 121 121 121 121 121
## [53806] 121 121 121 129 146 156 168 177 181 182 182 182 182 182 182 182 182
## [53823] 197 210 234 243 243 249 247 245 245 243 243 243 243 243 243 243 243
## [53840] 243 243 243 276 292 304 304 304 304 274 243 268 275 260 238 182 184
## [53857] 183 188 201 209 200 192 186 164 167 143 152 126 122 122 121 121 121
## [53874] 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121
## [53891] 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121
## [53908] 121 121 121 121 118 115 114 114 117 121 121 121 121 121 121 117  97
## [53925]  84  72  60  60  60  60  60  60  60  71  75  76  76  72  68  67  65
## [53942]  64  61  60  60  60  60  60  60  60  60  60  56  54  42  29  35  38
## [53959]  39  39  39  39  40  42  45  46  46  46  47  49  49  52  53  53  53
## [53976]  52  52  53  53  53  53  53  56  57  57  57  57  57  58  58  58  58
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## [80071]  49  50  51  51  53  54  55  56  56  57  58  60  60  60  60  60  60
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## [80377]  40  38  45  46  46  46  46  46  48  48  50  50  50  50  52  52  52
## [80394]  54  55  55  55  53  54  55  55  55  55  57  57  57  58  58  58  58
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## [97989]   2  11  17  21  23  23  22  21  24  26  32  36  38  42  49  49  28
## [98006]  26  25   2   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98023]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98040]   0   0   0   0   0   0   0   0   0   0   2   4   6   8  10  11  13
## [98057]  15  16  17  17  18  18  19  20  21  21  22  23  24  24  25  25  26
## [98074]  27  29  30  31  32  33  34  35  36  37  38  39  40  41  42  44  45
## [98091]  46  47  48  49  51  52  53  54  55  56  57  59  60  67  75  84  93
## [98108] 108 121 121 129 137 144 151 162 172 177 182 182 182 185 189 192 192
## [98125] 194 194 195 189 172 151 139 128 121 121 121 121 121 121 149 173 182
## [98142] 182 182 182 182 190 189 187 183 182 203 218 230 239 243 247 250 253
## [98159] 256 261 262 267 270 263 254 243 225 206 195 186 173 149 129 121 121
## [98176] 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121
## [98193] 121 121 121 162 182 179 182 182 180 181 182 182 182 195 226 239 243
## [98210] 243 243 243 244 243 182 185 182 198 221 243 243 243 243 243 243 203
## [98227] 182 182 182 243 237 242 243 243 236 217 201 189 176 163 166 169 173
## [98244] 177 180 184 187 182 187 188 182 186 190 183 182 191 202 218 234 243
## [98261] 243 243 243 243 243 243 243 243 243 243 243 243 248 268 281 296 304
## [98278] 287 279 273 266 260 253 267 285 304 305 305 305 304 277 243 243 243
## [98295] 258 277 304 304 304 304 304 304 304 297 275 259 249 248 253 265 282
## [98312] 297 302 303 304 304 304 304 304 304 304 304 304 341 365 366 365 366
## [98329] 365 365 372 371 368 367 366 366 365 349 332 313 304 270 243 229 227
## [98346] 230 243 225 204 186 166 149 135 121 121 151 172 160 148 135 121 118
## [98363] 109  99  92  85  78  71  65  60  60  60  60  60  60  60  60  60  60
## [98380]  60  60  60  60  60  60  60  60  60  60  56  49  47  47  51  52  51
## [98397]  51  51  51  52  52  53  53  53  53  54  55  55  56  56  56  56  55
## [98414]  56  56  56  56  56  57  57  58  58  58  59  59  59  59  59  59  60
## [98431]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [98448]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [98465]  60  60  60  60  60  60  60  60  60  55  57  60  64  68  73  78  79
## [98482]  89   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98499]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98516]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98533]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98550]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98567]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98584]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98601]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98618]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98635]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98652]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98669]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98686]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98703]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98720]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98737]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98754]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [98771]   0   0   0   0   0   0   0   0   0   0   0   0  23  38  44  53  67
## [98788]  85  97 109 121 121 139 138 134 130 121 117 117 119 120 121 148 162
## [98805] 174 190 212 195 194 189 184 175 152 135 134 131 121 121 121 121 117
## [98822] 115 113  98  89  65  60  72  77  80  73  60  61  60  60  60  60  60
## [98839]  56  50  45  41  37  32  26  20  16  11   8   4   4   5  13  16  23
## [98856]  25  32  40  50  55  55  52  53  55  58  60  60  66  89 108 134 176
## [98873] 181 185 189 193 197 203 213 204 230 249 250 251 252 255 261 286 298
## [98890] 310 331 352 365 377 386 393 398 402 409 420 431 433 446 470 487 487
## [98907] 487 487 479 464 441 416 396 375 356 336 304 274 253 243 260 304 320
## [98924] 339 347 353 365 381 396 412 414 394 379 374 369 356 369 398 426 417
## [98941] 412 413 419 426 447 463 475 487 480 482 487 490 487 503 513 527 540
## [98958] 548 548 548 551 548 524 503 487 512 528 548 497 474 470 468 467 471
## [98975] 476 502 523 536 548 548 548 523 500 487 467 487 521 548 561 562 556
## [98992] 548 528 507 472 426 426 426 406 385 365 321 291 275 257 243 220 201
## [99009] 192 182 157 121 101  60  60  60  60  79 100 121 122 101  60  60  60
## [99026]  60  67  60  63  60  61  60  60  60  60  60  60  60  60  60  60  60
## [99043]  60  60  60  60  60  58  55  54  52  50  49  46  43  42  40  38  36
## [99060]  35  33  30  28  26  25  23  21  18  16  15  13  11  10   8   5   3
## [99077]   2   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99094]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99111]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99128]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99145]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99162]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99179]   0   0   0   0   0   0   0   0   0   0   0   0   1   5   7   8   8
## [99196]   6   0   0   9  17  23  25  28  35  34  21  21  21   2   0   0   0
## [99213]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99230]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99247]   0   0   0   0   2   4   6   8  10  11  13  15  16  16  17  17  18
## [99264]  19  19  20  21  21  22  23  24  24  25  25  26  28  29  30  31  32
## [99281]  33  34  35  37  38  39  40  41  42  43  45  46  47  48  49  50  52
## [99298]  53  54  55  56  57  59  60  63  69  77  87 101 114 121 128 135 142
## [99315] 149 159 168 174 178 182 182 186 191 195 198 201 203 207 205 194 182
## [99332] 182 160 139 121 121 121 121 121 143 157 176 182 182 182 184 185 182
## [99349] 182 182 201 207 220 234 243 247 250 253 256 259 270 282 292 304 285
## [99366] 270 255 237 218 206 195 182 170 145 121 121 121 121 121 121 121 121
## [99383] 121 121 121 121 121 121 121 121 121 121 121 121 121 146 170 179 172
## [99400] 169 170 176 181 182 182 182 199 217 234 243 243 243 243 243 243 196
## [99417] 182 183 182 199 224 238 243 243 243 243 213 182 182 192 213 243 242
## [99434] 243 243 232 211 188 181 166 155 158 162 168 175 180 182 182 184 182
## [99451] 184 182 183 182 185 182 197 211 222 239 242 243 243 243 243 243 243
## [99468] 243 243 243 243 243 242 243 255 259 269 269 263 262 259 253 243 246
## [99485] 243 267 288 304 304 304 304 287 243 243 243 243 274 288 304 304 304
## [99502] 304 304 304 277 256 243 246 243 243 263 285 301 303 304 304 304 304
## [99519] 304 304 304 304 304 309 318 342 356 360 363 365 365 367 368 367 366
## [99536] 366 365 365 365 356 326 309 294 260 242 238 241 242 243 218 190 172
## [99553] 159 145 140 153 172 196 189 174 159 140 126 116 104  95  87  79  71
## [99570]  65  61  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [99587]  60  60  60  60  56  50  48  47  52  52  52  52  51  51  52  52  53
## [99604]  53  53  53  55  55  55  56  56  56  56  55  56  56  56  56  56  57
## [99621]  57  58  58  59  59  59  59  59  59  59  60  60  60  60  60  60  60
## [99638]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [99655]  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60  60
## [99672]  60  60  60  55  57  60  64  69  73  78  79  89   0   0   0   0   0
## [99689]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99706]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99723]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99740]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99757]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99774]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99791]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99808]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99825]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99842]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99859]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99876]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99893]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99910]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99927]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99944]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99961]   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
## [99978]   0   0   0   0   0   0   0  16  27  38  55  73  85  97 102 114 121
## [99995] 121 121 121 113 115
##  [ reached getOption("max.print") -- omitted 1342402 entries ]

Explore the Structure

And we could even then turn that vector back into a matrix of the proper dimensions.

#coerce our whole raser's dataset to a matrix, with the appropriate number
#of columns, and 
matrix(DEM[,], ncol = ncol(DEM), byrow = TRUE)
##         [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
##    [1,]  120  120  117  111  104   98   92   89   87    85    82    80
##    [2,]  123  123  118  109  102   96   89   85   83    82    81    80
##    [3,]  127  127  119  113  106   99   92   88   86    84    81    79
##    [4,]  130  130  125  119  113  108  101   97   94    90    83    77
##    [5,]  130  131  128  123  120  115  110  107  104    97    87    77
##    [6,]  126  128  125  122  120  118  116  114  111   103    91    78
##    [7,]  115  123  116  113  111  110  109  108  103    92    79    68
##    [8,]   99   97  102   97   95   95   95   93   86    76    67    57
##    [9,]   77   74   78   74   73   73   74   73   60    58    46    38
##   [10,]   50   47   48   49   48   50   51   51   49    48    38    27
##   [11,]   23   10   18   19   19   28   28   31   38    42    37    27
##   [12,]    0    3    9   10   10   11   11   17   29    38    37    25
##   [13,]    0    0    1    2    2    2    2   13   26    35    34    22
##   [14,]    0    0    0    0    0    0    0   11   23    31    30    19
##   [15,]    0    0    0    0    0    0    0   10   21    28    27    18
##   [16,]    0    0    0    0    0    0    0    9   19    24    23    17
##   [17,]    0    0    0    0    0    0    0    7   16    20    20    15
##   [18,]    0    0    0    0    0    0    0    6   13    16    16    13
##   [19,]    0    0    0    0    0    0    0    4   10    12    13    11
##   [20,]    0    0    0    0    0    0    0    3    7     8     8     8
##   [21,]    0    0    0    0    0    0    0    1    3     3     4     4
##   [22,]    0    0    0    0    0    0    0    0    0     0     1     1
##   [23,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [24,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [25,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [26,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [27,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [28,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [29,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [30,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [31,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [32,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [33,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [34,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [35,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [36,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [37,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [38,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [39,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [40,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [41,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [42,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [43,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [44,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [45,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [46,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [47,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [48,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [49,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [50,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [51,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [52,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [53,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [54,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [55,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [56,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [57,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [58,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [59,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [60,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [61,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [62,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [63,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [64,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [65,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [66,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [67,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [68,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [69,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [70,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [71,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [72,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [73,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [74,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [75,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [76,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [77,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [78,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [79,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [80,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [81,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [82,]    0    0    0    0    0    0    0    0    0     0     0     0
##   [83,]    0    0    0    0    0    0    0    0    0     0     0     0
##         [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23]
##    [1,]    79    76    72    67    57    45    32    20    12     6     3
##    [2,]    79    76    72    67    57    45    32    19    11     6     3
##    [3,]    76    73    69    66    57    46    32    21    14     9     6
##    [4,]    72    68    66    64    60    52    42    32    23    18    13
##    [5,]    69    65    63    62    61    57    50    43    37    30    25
##    [6,]    68    62    61    60    60    59    56    52    48    44    38
##    [7,]    60    55    56    56    58    57    57    57    56    54    49
##    [8,]    48    44    45    46    51    51    53    56    57    57    56
##    [9,]    35    31    31    37    40    40    45    50    52    51    52
##   [10,]    23    19    18    22    26    26    33    39    41    39    41
##   [11,]    17    11     9    12    13    13    18    24    25    23    26
##   [12,]    15     9     6     5     6     4     7    10    11     9    11
##   [13,]    13     8     5     3     2     1     1     2     2     2     2
##   [14,]    12     8     5     3     2     1     0     0     0     0     0
##   [15,]    11     7     5     4     2     1     1     0     0     0     0
##   [16,]    11     7     5     4     3     2     1     0     0     0     0
##   [17,]    10     7     6     5     3     2     1     1     0     0     0
##   [18,]    10     8     7     5     4     3     2     1     0     0     0
##   [19,]     9     8     7     5     4     3     2     1     0     0     0
##   [20,]     7     6     5     5     3     2     1     1     0     0     0
##   [21,]     4     4     3     3     2     1     0     0     0     0     0
##   [22,]     1     1     1     1     0     0     0     0     0     0     0
##   [23,]     0     0     0     0     0     0     0     0     0     0     0
##   [24,]     0     0     0     0     0     0     0     0     0     0     0
##   [25,]     0     0     0     0     0     0     0     0     0     0     0
##   [26,]     0     0     0     0     0     0     0     0     0     0     0
##   [27,]     0     0     0     0     0     0     0     0     0     0     0
##   [28,]     0     0     0     0     0     0     0     0     0     0     0
##   [29,]     0     0     0     0     0     0     0     0     0     0     0
##   [30,]     0     0     0     0     0     0     0     0     0     0     0
##   [31,]     0     0     0     0     0     0     0     0     0     0     0
##   [32,]     0     0     0     0     0     0     0     0     0     0     0
##   [33,]     0     0     0     0     0     0     0     0     0     0     0
##   [34,]     0     0     0     0     0     0     0     0     0     0     0
##   [35,]     0     0     0     0     0     0     0     0     0     0     0
##   [36,]     0     0     0     0     0     0     0     0     0     0     0
##   [37,]     0     0     0     0     0     0     0     0     0     0     0
##   [38,]     0     0     0     0     0     0     0     0     0     0     0
##   [39,]     0     0     0     0     0     0     0     0     0     0     0
##   [40,]     0     0     0     0     0     0     0     0     0     0     0
##   [41,]     0     0     0     0     0     0     0     0     0     0     0
##   [42,]     0     0     0     0     0     0     0     0     0     0     0
##   [43,]     0     0     0     0     0     0     0     0     0     0     0
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##   [46,]     0     0     0     0     0     0     0     0     0     0     0
##   [47,]     0     0     0     0     0     0     0     0     0     0     0
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##   [50,]     0     0     0     0     0     0     0     0     0     0     0
##   [51,]     0     0     0     0     0     0     0     0     0     0     0
##   [52,]     0     0     0     0     0     0     0     0     0     0     0
##   [53,]     0     0     0     0     0     0     0     0     0     0     0
##   [54,]     0     0     0     0     0     0     0     0     0     0     0
##   [55,]     0     0     0     0     0     0     0     0     0     0     0
##   [56,]     0     0     0     0     0     0     0     0     0     0     0
##   [57,]     0     0     0     0     0     0     0     0     0     0     0
##   [58,]     0     0     0     0     0     0     0     0     0     0     0
##   [59,]     0     0     0     0     0     0     0     0     0     0     0
##   [60,]     0     0     0     0     0     0     0     0     0     0     0
##   [61,]     0     0     0     0     0     0     0     0     0     0     0
##   [62,]     0     0     0     0     0     0     0     0     0     0     0
##   [63,]     0     0     0     0     0     0     0     0     0     0     0
##   [64,]     0     0     0     0     0     0     0     0     0     0     0
##   [65,]     0     0     0     0     0     0     0     0     0     0     0
##   [66,]     0     0     0     0     0     0     0     0     0     0     0
##   [67,]     0     0     0     0     0     0     0     0     0     0     0
##   [68,]     0     0     0     0     0     0     0     0     0     0     0
##   [69,]     0     0     0     0     0     0     0     0     0     0     0
##   [70,]     0     0     0     0     0     0     0     0     0     0     0
##   [71,]     0     0     0     0     0     0     0     0     0     0     0
##   [72,]     0     0     0     0     0     0     0     0     0     0     0
##   [73,]     0     0     0     0     0     0     0     0     0     0     0
##   [74,]     0     0     0     0     0     0     0     0     0     0     0
##   [75,]     0     0     0     0     0     0     0     0     0     0     0
##   [76,]     0     0     0     0     0     0     0     0     0     0     0
##   [77,]     0     0     0     0     0     0     0     0     0     0     0
##   [78,]     0     0     0     0     0     0     0     0     0     0     0
##   [79,]     0     0     0     0     0     0     0     0     0     0     0
##   [80,]     0     0     0     0     0     0     0     0     0     0     0
##   [81,]     0     0     0     0     0     0     0     0     0     0     0
##   [82,]     0     0     0     0     0     0     0     0     0     0     0
##   [83,]     0     0     0     0     0     0     0     0     0     0     0
##         [,24] [,25] [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34]
##    [1,]     1     0     0     0     0     0     0     0     0     0     0
##    [2,]     1     0     0     0     0     0     0     0     0     0     0
##    [3,]     3     1     0     0     0     0     0     0     0     0     0
##    [4,]     8     5     2     1     0     0     0     0     0     0     0
##    [5,]    17    11     7     4     2     1     0     0     0     0     0
##    [6,]    28    21    14     8     4     2     1     0     0     0     0
##    [7,]    40    33    23    15     9     5     2     0     0     0     0
##    [8,]    50    43    33    23    15     8     4     1     0     0     1
##    [9,]    47    46    40    32    20    11     5     1     1     2     5
##   [10,]    38    36    27    21    15     9     4     1     2     6    13
##   [11,]    23    23    17    12     8     5     2     1     3    11    23
##   [12,]     9    10     7     4     2     1     0     0     3    17    38
##   [13,]     2     2     2     1     0     0     0     0     0     7    25
##   [14,]     0     0     0     0     0     0     0     0     0     1    10
##   [15,]     0     0     0     0     0     0     0     0     0     0     2
##   [16,]     0     0     0     0     0     0     0     0     0     0     0
##   [17,]     0     0     0     0     0     0     0     0     0     0     0
##   [18,]     0     0     0     0     0     0     0     0     0     0     0
##   [19,]     0     0     0     0     0     0     0     0     0     0     0
##   [20,]     0     0     0     0     0     0     0     0     0     0     0
##   [21,]     0     0     0     0     0     0     0     0     0     0     0
##   [22,]     0     0     0     0     0     0     0     0     0     0     0
##   [23,]     0     0     0     0     0     0     0     0     0     0     0
##   [24,]     0     0     0     0     0     0     0     0     0     0     0
##   [25,]     0     0     0     0     0     0     0     0     0     0     0
##   [26,]     0     0     0     0     0     0     0     0     0     0     0
##   [27,]     0     0     0     0     0     0     0     0     0     0     0
##   [28,]     0     0     0     0     0     0     0     0     0     0     0
##   [29,]     0     0     0     0     0     0     0     0     0     0     0
##   [30,]     0     0     0     0     0     0     0     0     0     0     0
##   [31,]     0     0     0     0     0     0     0     0     0     0     0
##   [32,]     0     0     0     0     0     0     0     0     0     0     0
##   [33,]     0     0     0     0     0     0     0     0     0     0     0
##   [34,]     0     0     0     0     0     0     0     0     0     0     0
##   [35,]     0     0     0     0     0     0     0     0     0     0     0
##   [36,]     0     0     0     0     0     0     0     0     0     0     0
##   [37,]     0     0     0     0     0     0     0     0     0     0     0
##   [38,]     0     0     0     0     0     0     0     0     0     0     0
##   [39,]     0     0     0     0     0     0     0     0     0     0     0
##   [40,]     0     0     0     0     0     0     0     0     0     0     0
##   [41,]     0     0     0     0     0     0     0     0     0     0     0
##   [42,]     0     0     0     0     0     0     0     0     0     0     0
##   [43,]     0     0     0     0     0     0     0     0     0     0     0
##   [44,]     0     0     0     0     0     0     0     0     0     0     0
##   [45,]     0     0     0     0     0     0     0     0     0     0     0
##   [46,]     0     0     0     0     0     0     0     0     0     0     0
##   [47,]     0     0     0     0     0     0     0     0     0     0     0
##   [48,]     0     0     0     0     0     0     0     0     0     0     0
##   [49,]     0     0     0     0     0     0     0     0     0     0     0
##   [50,]     0     0     0     0     0     0     0     0     0     0     0
##   [51,]     0     0     0     0     0     0     0     0     0     0     0
##   [52,]     0     0     0     0     0     0     0     0     0     0     0
##   [53,]     0     0     0     0     0     0     0     0     0     0     0
##   [54,]     0     0     0     0     0     0     0     0     0     0     0
##   [55,]     0     0     0     0     0     0     0     0     0     0     0
##   [56,]     0     0     0     0     0     0     0     0     0     0     0
##   [57,]     0     0     0     0     0     0     0     0     0     0     0
##   [58,]     0     0     0     0     0     0     0     0     0     0     0
##   [59,]     0     0     0     0     0     0     0     0     0     0     0
##   [60,]     0     0     0     0     0     0     0     0     0     0     0
##   [61,]     0     0     0     0     0     0     0     0     0     0     0
##   [62,]     0     0     0     0     0     0     0     0     0     0     0
##   [63,]     0     0     0     0     0     0     0     0     0     0     0
##   [64,]     0     0     0     0     0     0     0     0     0     0     0
##   [65,]     0     0     0     0     0     0     0     0     0     0     0
##   [66,]     0     0     0     0     0     0     0     0     0     0     0
##   [67,]     0     0     0     0     0     0     0     0     0     0     0
##   [68,]     0     0     0     0     0     0     0     0     0     0     0
##   [69,]     0     0     0     0     0     0     0     0     0     0     0
##   [70,]     0     0     0     0     0     0     0     0     0     0     0
##   [71,]     0     0     0     0     0     0     0     0     0     0     0
##   [72,]     0     0     0     0     0     0     0     0     0     0     0
##   [73,]     0     0     0     0     0     0     0     0     0     0     0
##   [74,]     0     0     0     0     0     0     0     0     0     0     0
##   [75,]     0     0     0     0     0     0     0     0     0     0     0
##   [76,]     0     0     0     0     0     0     0     0     0     0     0
##   [77,]     0     0     0     0     0     0     0     0     0     0     0
##   [78,]     0     0     0     0     0     0     0     0     0     0     0
##   [79,]     0     0     0     0     0     0     0     0     0     0     0
##   [80,]     0     0     0     0     0     0     0     0     0     0     0
##   [81,]     0     0     0     0     0     0     0     0     0     0     0
##   [82,]     0     0     0     0     0     0     0     0     0     0     0
##   [83,]     0     0     0     0     0     0     0     0     0     0     0
##         [,35] [,36] [,37] [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45]
##    [1,]     0     0     0     0     0     0     0     0     0     0     0
##    [2,]     0     0     0     0     0     0     0     0     0     0     0
##    [3,]     0     0     0     0     0     0     0     0     0     0     0
##    [4,]     0     0     0     0     0     0     0     0     0     0     0
##    [5,]     0     0     0     0     0     0     0     0     0     0     0
##    [6,]     0     0     0     0     0     0     0     0     0     0     0
##    [7,]     0     0     1     1     0     0     0     0     0     0     0
##    [8,]     2     3     4     3     2     1     0     0     0     0     0
##    [9,]     7    11    11     8     5     3     1     0     0     0     0
##   [10,]    17    23    23    17    11     6     3     1     0     0     0
##   [11,]    28    36    36    31    20    11     5     2     0     0     0
##   [12,]    38    46    51    39    28    17     7     2     0     0     0
##   [13,]    41    52    44    29    19    11     5     1     0     0     0
##   [14,]    31    32    30    17     9     5     2     0     0     0     0
##   [15,]     9    14    14     8     4     2     1     0     0     0     0
##   [16,]     1     4     4     2     1     0     0     0     0     0     0
##   [17,]     0     0     1     0     0     0     0     0     0     0     0
##   [18,]     0     0     0     0     0     0     0     0     0     0     0
##   [19,]     0     0     0     0     0     0     0     0     0     0     0
##   [20,]     0     0     0     0     0     0     0     0     0     0     0
##   [21,]     0     0     0     0     0     0     0     0     0     0     0
##   [22,]     0     0     0     0     0     0     0     0     0     0     0
##   [23,]     0     0     0     0     0     0     0     0     0     0     0
##   [24,]     0     0     0     0     0     0     0     0     0     0     0
##   [25,]     0     0     0     0     0     0     0     0     0     0     0
##   [26,]     0     0     0     0     0     0     0     0     0     0     0
##   [27,]     0     0     0     0     0     0     0     0     0     0     0
##   [28,]     0     0     0     0     0     0     0     0     0     0     0
##   [29,]     0     0     0     0     0     0     0     0     0     0     0
##   [30,]     0     0     0     0     0     0     0     0     0     0     0
##   [31,]     0     0     0     0     0     0     0     0     0     0     0
##   [32,]     0     0     0     0     0     0     0     0     0     0     0
##   [33,]     0     0     0     0     0     0     0     0     0     0     0
##   [34,]     0     0     0     0     0     0     0     0     0     0     0
##   [35,]     0     0     0     0     0     0     0     0     0     0     0
##   [36,]     0     0     0     0     0     0     0     0     0     0     0
##   [37,]     0     0     0     0     0     0     0     0     0     0     0
##   [38,]     0     0     0     0     0     0     0     0     0     0     0
##   [39,]     0     0     0     0     0     0     0     0     0     0     0
##   [40,]     0     0     0     0     0     0     0     0     0     0     0
##   [41,]     0     0     0     0     0     0     0     0     0     0     0
##   [42,]     0     0     0     0     0     0     0     0     0     0     0
##   [43,]     0     0     0     0     0     0     0     0     0     0     0
##   [44,]     0     0     0     0     0     0     0     0     0     0     0
##   [45,]     0     0     0     0     0     0     0     0     0     0     0
##   [46,]     0     0     0     0     0     0     0     0     0     0     0
##   [47,]     0     0     0     0     0     0     0     0     0     0     0
##   [48,]     0     0     0     0     0     0     0     0     0     0     0
##   [49,]     0     0     0     0     0     0     0     0     0     0     0
##   [50,]     0     0     0     0     0     0     0     0     0     0     0
##   [51,]     0     0     0     0     0     0     0     0     0     0     0
##   [52,]     0     0     0     0     0     0     0     0     0     0     0
##   [53,]     0     0     0     0     0     0     0     0     0     0     0
##   [54,]     0     0     0     0     0     0     0     0     0     0     0
##   [55,]     0     0     0     0     0     0     0     0     0     0     0
##   [56,]     0     0     0     0     0     0     0     0     0     0     0
##   [57,]     0     0     0     0     0     0     0     0     0     0     0
##   [58,]     0     0     0     0     0     0     0     0     0     0     0
##   [59,]     0     0     0     0     0     0     0     0     0     0     0
##   [60,]     0     0     0     0     0     0     0     0     0     0     0
##   [61,]     0     0     0     0     0     0     0     0     0     0     0
##   [62,]     0     0     0     0     0     0     0     0     0     0     0
##   [63,]     0     0     0     0     0     0     0     0     0     0     0
##   [64,]     0     0     0     0     0     0     0     0     0     0     0
##   [65,]     0     0     0     0     0     0     0     0     0     0     0
##   [66,]     0     0     0     0     0     0     0     0     0     0     0
##   [67,]     0     0     0     0     0     0     0     0     0     0     0
##   [68,]     0     0     0     0     0     0     0     0     0     0     0
##   [69,]     0     0     0     0     0     0     0     0     0     0     0
##   [70,]     0     0     0     0     0     0     0     0     0     0     0
##   [71,]     0     0     0     0     0     0     0     0     0     0     0
##   [72,]     0     0     0     0     0     0     0     0     0     0     0
##   [73,]     0     0     0     0     0     0     0     0     0     0     0
##   [74,]     0     0     0     0     0     0     0     0     0     0     0
##   [75,]     0     0     0     0     0     0     0     0     0     0     0
##   [76,]     0     0     0     0     0     0     0     0     0     0     0
##   [77,]     0     0     0     0     0     0     0     0     0     0     0
##   [78,]     0     0     0     0     0     0     0     0     0     0     0
##   [79,]     0     0     0     0     0     0     0     0     0     0     0
##   [80,]     0     0     0     0     0     0     0     0     0     0     0
##   [81,]     0     0     0     0     0     0     0     0     0     0     0
##   [82,]     0     0     0     0     0     0     0     0     0     0     0
##   [83,]     0     0     0     0     0     0     0     0     0     0     0
##         [,46] [,47] [,48] [,49] [,50] [,51] [,52] [,53] [,54] [,55] [,56]
##    [1,]     0     0     0     0     0     0     0     0     0     0     0
##    [2,]     0     0     0     0     0     0     0     0     0     0     0
##    [3,]     0     0     0     0     0     0     0     0     0     0     0
##    [4,]     0     0     0     0     0     0     0     0     0     0     0
##    [5,]     0     0     0     0     0     0     0     0     0     0     0
##    [6,]     0     0     0     0     0     0     0     0     0     0     0
##    [7,]     0     0     0     0     0     0     0     0     0     0     0
##    [8,]     0     0     0     0     0     0     0     0     0     0     0
##    [9,]     0     0     0     0     0     0     0     0     0     0     0
##   [10,]     0     0     0     0     0     0     0     0     0     0     0
##   [11,]     0     0     0     0     0     0     0     0     0     0     0
##   [12,]     0     0     0     0     0     0     0     0     0     0     0
##   [13,]     0     0     0     0     0     0     0     0     0     0     0
##   [14,]     0     0     0     0     0     0     0     0     0     0     0
##   [15,]     0     0     0     0     0     0     0     0     0     0     0
##   [16,]     0     0     0     0     0     0     0     0     0     0     0
##   [17,]     0     0     0     0     0     0     0     0     0     0     0
##   [18,]     0     0     0     0     0     0     0     0     0     0     0
##   [19,]     0     0     0     0     0     0     0     0     0     0     0
##   [20,]     0     0     0     0     0     0     0     0     0     0     0
##   [21,]     0     0     0     0     0     0     0     0     0     0     0
##   [22,]     0     0     0     0     0     0     0     0     0     0     0
##   [23,]     0     0     0     0     0     0     0     0     0     0     0
##   [24,]     0     0     0     0     0     0     0     0     0     0     0
##   [25,]     0     0     0     0     0     0     0     0     0     0     0
##   [26,]     0     0     0     0     0     0     0     0     0     0     0
##   [27,]     0     0     0     0     0     0     0     0     0     0     0
##   [28,]     0     0     0     0     0     0     0     0     0     0     0
##   [29,]     0     0     0     0     0     0     0     0     0     0     0
##   [30,]     0     0     0     0     0     0     0     0     0     0     0
##   [31,]     0     0     0     0     0     0     0     0     0     0     0
##   [32,]     0     0     0     0     0     0     0     0     0     0     0
##   [33,]     0     0     0     0     0     0     0     0     0     0     0
##   [34,]     0     0     0     0     0     0     0     0     0     0     0
##   [35,]     0     0     0     0     0     0     0     0     0     0     0
##   [36,]     0     0     0     0     0     0     0     0     0     0     0
##   [37,]     0     0     0     0     0     0     0     0     0     0     0
##   [38,]     0     0     0     0     0     0     0     0     0     0     0
##   [39,]     0     0     0     0     0     0     0     0     0     0     0
##   [40,]     0     0     0     0     0     0     0     0     0     0     0
##   [41,]     0     0     0     0     0     0     0     0     0     0     0
##   [42,]     0     0     0     0     0     0     0     0     0     0     0
##   [43,]     0     0     0     0     0     0     0     0     0     0     0
##   [44,]     0     0     0     0     0     0     0     0     0     0     0
##   [45,]     0     0     0     0     0     0     0     0     0     0     0
##   [46,]     0     0     0     0     0     0     0     0     0     0     0
##   [47,]     0     0     0     0     0     0     0     0     0     0     0
##   [48,]     0     0     0     0     0     0     0     0     0     0     0
##   [49,]     0     0     0     0     0     0     0     0     0     0     0
##   [50,]     0     0     0     0     0     0     0     0     0     0     0
##   [51,]     0     0     0     0     0     0     0     0     0     0     0
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##         [,68] [,69] [,70] [,71] [,72] [,73] [,74] [,75] [,76] [,77] [,78]
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##         [,79] [,80] [,81] [,82] [,83] [,84] [,85] [,86] [,87] [,88] [,89]
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##         [,200] [,201] [,202] [,203] [,204] [,205] [,206] [,207] [,208]
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##   [83,]      0      0      0      0      0      0      0      0      0
##         [,209] [,210] [,211] [,212] [,213] [,214] [,215] [,216] [,217]
##    [1,]     19     27     33     40     51     59     70     69     91
##    [2,]     16     23     29     36     49     56     61     64     88
##    [3,]     11     17     23     29     39     48     55     67     77
##    [4,]      5     10     14     20     28     37     45     56     70
##    [5,]      1      3      5      9     17     25     33     42     51
##    [6,]      0      0      1      2      7     13     21     29     36
##    [7,]      0      0      0      0      1      5     11     18     24
##    [8,]      0      0      0      0      0      1      4      9     14
##    [9,]      0      0      0      0      0      0      0      3      7
##   [10,]      0      0      0      0      0      0      0      0      1
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##   [82,]      0      0      0      0      0      0      0      0      0
##   [83,]      0      0      0      0      0      0      0      0      0
##         [,218] [,219] [,220] [,221] [,222] [,223] [,224] [,225] [,226]
##    [1,]    108    123    140    158    168    185    196    204    205
##    [2,]    104    121    139    158    170    186    197    203    204
##    [3,]     99    116    132    148    163    174    184    192    196
##    [4,]     94    110    125    139    152    161    171    179    185
##    [5,]     64     75    100    120    134    145    156    163    170
##    [6,]     44     53     62     90    111    126    138    146    153
##    [7,]     31     38     49     68     89    106    118    129    136
##    [8,]     20     27     37     51     61     72     95    109    121
##    [9,]     12     18     28     40     55     62     87    101    108
##   [10,]      5     11     22     35     48     73     97    100     98
##   [11,]      1      5     14     27     51     78     98     91     81
##   [12,]      0      0      4     17     32     64     85     73     60
##   [13,]      0      0      0     11     25     53     72     64     62
##   [14,]      0      0      0      4     16     35     51     52     56
##   [15,]      0      0      0      0      6     14     29     43     53
##   [16,]      0      0      0      0      0      4     22     39     58
##   [17,]      0      0      0      0      0      0     11     33     60
##   [18,]      0      0      0      0      0      0      0      8     28
##   [19,]      0      0      0      0      0      0      0      0      0
##   [20,]      0      0      0      0      0      0      0      0      0
##   [21,]      0      0      0      0      0      0      0      0      0
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##   [24,]      0      0      0      0      0      0      0      0      0
##   [25,]      0      0      0      0      0      0      0      0      0
##   [26,]      0      0      0      0      0      0      0      0      0
##   [27,]      0      0      0      0      0      0      0      0      0
##   [28,]      0      0      0      0      0      0      0      0      0
##   [29,]      0      0      0      0      0      0      0      0      0
##   [30,]      0      0      0      0      0      0      0      0      0
##   [31,]      0      0      0      0      0      0      0      0      0
##   [32,]      0      0      0      0      0      0      0      0      0
##   [33,]      0      0      0      0      0      0      0      0      0
##   [34,]      0      0      0      0      0      0      0      0      0
##   [35,]      0      0      0      0      0      0      0      0      0
##   [36,]      0      0      0      0      0      0      0      0      0
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##         [,227] [,228] [,229] [,230] [,231] [,232] [,233] [,234] [,235]
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##    [2,]    203    193    186    180    169    159    149    134    117
##    [3,]    196    190    183    176    163    150    138    125    109
##    [4,]    185    183    174    167    152    136    123    108     91
##    [5,]    170    170    160    151    136    120    105     90     76
##    [6,]    153    153    141    129    116    103     88     75     68
##    [7,]    136    132    118    105     94     82     75     67     64
##    [8,]    117    103     82     70     75     70     66     63     61
##    [9,]     95     79     72     65     63     63     62     61     62
##   [10,]     84     72     65     62     61     61     60     63     71
##   [11,]     73     66     62     61     60     60     60     71     84
##   [12,]     60     62     61     60     60     60     60     87    107
##   [13,]     60     61     61     61     60     60     85    103    121
##   [14,]     58     60     61     66     74     95    111    134    146
##   [15,]     58     60     68     82     97    121    133    172    172
##   [16,]     60     60     72     82     94    112    131    172    170
##   [17,]     60     60     67     72     77     91    103    121    144
##   [18,]     46     50     50     52     57     68     72     77    104
##   [19,]     15     21     20     28     39     44     48     54     60
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##         [,236] [,237] [,238] [,239] [,240] [,241] [,242] [,243] [,244]
##    [1,]    101     81     69     62     54     50     53     53     54
##    [2,]    100     81     69     61     52     47     44     47     52
##    [3,]     90     77     67     60     52     47     46     50     54
##    [4,]     75     67     63     59     54     52     55     61     60
##    [5,]     68     64     62     60     58     62     73     72     72
##    [6,]     64     62     61     61     67     81    100     99     90
##    [7,]     61     61     62     63     78     98    110    114    106
##    [8,]     61     62     71     74     91    107    117    121    116
##    [9,]     65     75     85     89    101    114    126    133    127
##   [10,]     80    100    103    108    118    128    140    147    140
##   [11,]     97    112    124    130    139    146    159    162    155
##   [12,]    121    135    146    152    161    168    182    177    182
##   [13,]    135    149    163    170    182    180    178    182    182
##   [14,]    156    174    180    182    181    182    183    183    183
##   [15,]    167    182    182    181    182    184    186    188    188
##   [16,]    161    163    175    182    182    185    192    198    204
##   [17,]    138    140    153    168    182    187    202    215    226
##   [18,]    110    118    129    147    164    189    213    236    243
##   [19,]     78    100    115    121    141    175    206    222    235
##   [20,]     60     86    111    120    130    168    188    211    226
##   [21,]     60     86    121    119    138    170    182    201    223
##   [22,]     52     68     87    111    131    175    194    209    236
##   [23,]     30     45     60     87    121    148    182    200    205
##   [24,]     15     31     47     60     95    131    161    182    182
##   [25,]      0      9     28     51     68    100    131    146    158
##   [26,]      0      0      0     26     43     70    101    121    137
##   [27,]      0      0      0      5     21     45     71     91    112
##   [28,]      0      0      0      0      0     22     45     60     87
##   [29,]      0      0      0      0      0      3     22     37     53
##   [30,]      0      0      0      0      0      0      0     14     31
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##   [83,]      0      0      0      0      0      0      0      0      0
##         [,245] [,246] [,247] [,248] [,249] [,250] [,251] [,252] [,253]
##    [1,]     56     58     74     91    107    126    143    162    174
##    [2,]     56     59     75     92    107    126    143    160    172
##    [3,]     58     61     70     87    103    118    133    146    162
##    [4,]     61     61     63     76     94    106    121    131    137
##    [5,]     68     64     63     74     91    105    116    122    127
##    [6,]     82     73     71     80     96    109    124    130    136
##    [7,]     98     86     83     93    107    127    139    145    153
##    [8,]    109     99     96    102    111    143    159    169    174
##    [9,]    119    111    109    112    116    128    145    160    174
##   [10,]    131    123    120    120    121    123    130    140    158
##   [11,]    143    133    132    129    130    127    124    129    146
##   [12,]    166    156    144    140    143    135    121    121    142
##   [13,]    182    176    173    182    165    157    147    144    150
##   [14,]    182    182    182    191    188    185    174    165    167
##   [15,]    182    182    182    205    204    199    192    182    182
##   [16,]    200    197    215    223    219    216    211    210    206
##   [17,]    224    229    238    238    235    233    233    235    243
##   [18,]    243    243    243    243    242    241    241    243    243
##   [19,]    242    243    243    243    243    243    243    243    243
##   [20,]    237    242    243    243    243    243    243    243    243
##   [21,]    237    243    243    243    243    243    243    243    243
##   [22,]    243    242    243    243    243    243    243    243    243
##   [23,]    223    243    243    243    243    243    243    243    243
##   [24,]    182    208    237    243    243    243    243    243    243
##   [25,]    169    179    209    243    243    243    243    243    243
##   [26,]    152    169    194    227    243    243    243    243    243
##   [27,]    131    158    190    218    243    243    243    243    243
##   [28,]    121    137    170    200    220    243    243    243    243
##   [29,]     75    106    141    172    192    195    198    198    218
##   [30,]     48     60    109    142    155    161    162    173    182
##   [31,]     28     51     81    113    129    131    131    146    156
##   [32,]      0     26     66     89     96    104    113    121    121
##   [33,]      0      0     48     75     78     87     95     98    109
##   [34,]      0      0     26     51     57     67     69     70     73
##   [35,]      0      0     10     30     41     48     52     54     58
##   [36,]      0      0      2     15     28     34     39     45     52
##   [37,]      0      0      0      0     15     22     29     37     47
##   [38,]      0      0      0      0      3     11     20     31     47
##   [39,]      0      0      0      0      0      0     11     30     55
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##   [83,]      0      0      0      0      0      0      0      0      0
##         [,254] [,255] [,256] [,257] [,258] [,259] [,260] [,261] [,262]
##    [1,]    202    223    234    246    260    282    308    336    367
##    [2,]    201    223    232    240    257    280    304    334    366
##    [3,]    185    206    223    235    250    268    292    322    353
##    [4,]    156    171    188    208    226    244    269    297    321
##    [5,]    141    158    171    186    205    222    242    271    294
##    [6,]    142    155    173    185    202    212    227    257    282
##    [7,]    160    173    186    198    206    219    241    266    285
##    [8,]    183    192    207    225    236    248    271    288    300
##    [9,]    192    212    228    242    260    276    289    295    305
##   [10,]    182    203    224    245    274    285    287    294    303
##   [11,]    168    190    212    231    250    267    275    286    296
##   [12,]    159    182    194    211    227    243    256    275    287
##   [13,]    165    176    182    197    215    231    243    257    272
##   [14,]    172    177    180    182    198    220    234    242    251
##   [15,]    178    180    181    181    182    213    231    239    243
##   [16,]    198    192    182    201    212    221    237    249    277
##   [17,]    243    243    243    243    243    243    251    277    304
##   [18,]    243    243    243    243    243    255    267    293    302
##   [19,]    243    243    243    243    243    257    269    293    304
##   [20,]    243    243    243    243    243    252    259    273    291
##   [21,]    243    243    243    243    243    243    243    259    261
##   [22,]    243    243    243    243    243    243    239    243    243
##   [23,]    243    243    243    243    243    243    230    227    231
##   [24,]    243    243    243    243    243    243    218    213    220
##   [25,]    243    243    243    243    243    243    202    199    210
##   [26,]    243    243    243    243    243    243    192    182    199
##   [27,]    243    243    243    243    226    192    186    182    192
##   [28,]    243    243    243    216    202    182    182    182    189
##   [29,]    232    231    215    200    182    174    174    180    184
##   [30,]    200    201    194    182    144    148    161    174    181
##   [31,]    173    186    169    147    121    121    145    167    178
##   [32,]    142    144    142    121    126    122    131    156    167
##   [33,]    121    129    121    122    121    123    129    150    161
##   [34,]     92    102    107    112    118    121    129    144    154
##   [35,]     60     60     78     97    111    121    133    144    153
##   [36,]     57     59     60     70    101    121    132    143    151
##   [37,]     54     58     59     60     90    121    128    139    147
##   [38,]     54     58     60     68     86    104    124    134    142
##   [39,]     60     60     63     75     89    100    116    130    138
##   [40,]     60     60     66     76     87     98    116    128    136
##   [41,]     60     60     70     78     87     97    115    125    132
##   [42,]     60     60     68     76     84     93    106    118    125
##   [43,]     40     60     65     71     78     87     99    110    116
##   [44,]     27     44     60     66     73     81     94    106    112
##   [45,]      7     27     43     56     64     73     86    100    108
##   [46,]      0     12     30     47     60     67     81     95    105
##   [47,]      0      4     20     38     54     63     75     92    104
##   [48,]      0      0      8     27     41     52     66     90    106
##   [49,]      0      0      0     15     32     47     63     86    106
##   [50,]      0      0      0      8     25     43     67     92    109
##   [51,]      0      0      0      0     17     38     61     91    112
##   [52,]      0      0      0      0      8     30     56     79     90
##   [53,]      0      0      0      0      0     30     62     67     68
##   [54,]      0      0      0      0      0     25     60     60     60
##   [55,]      0      0      0      0      0     15     50     60     60
##   [56,]      0      0      0      0      0      0     41     60     60
##   [57,]      0      0      0      0      0      0     30     47     57
##   [58,]      0      0      0      0      0      0     22     45     53
##   [59,]      0      0      0      0      0      0     27     50     60
##   [60,]      0      0      0      0      0      0     30     60     58
##   [61,]      0      0      0      0      0      0     29     60     60
##   [62,]      0      0      0      0      0      0     25     51     60
##   [63,]      0      0      0      0      0      0     16     39     60
##   [64,]      0      0      0      0      0      0     11     33     60
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##   [82,]      0      0      0      0      0      0      0      0      0
##   [83,]      0      0      0      0      0      0      0      0      0
##         [,263] [,264] [,265] [,266] [,267] [,268] [,269] [,270] [,271]
##    [1,]    383    385    379    371    359    345    325    311    280
##    [2,]    382    385    381    373    360    345    325    311    280
##    [3,]    369    375    376    371    360    345    329    315    301
##    [4,]    343    358    367    368    362    350    339    329    316
##    [5,]    318    342    355    363    362    357    351    342    330
##    [6,]    302    325    346    358    363    363    362    355    344
##    [7,]    300    320    342    355    362    364    365    364    356
##    [8,]    313    329    347    358    363    365    365    365    364
##    [9,]    317    332    348    358    363    365    365    365    365
##   [10,]    314    330    347    358    363    365    365    365    365
##   [11,]    308    325    345    357    363    365    365    365    365
##   [12,]    296    304    330    365    365    365    365    365    365
##   [13,]    286    297    304    338    365    365    365    365    365
##   [14,]    276    293    304    322    336    348    350    347    332
##   [15,]    272    294    304    306    308    304    304    304    304
##   [16,]    294    303    306    310    316    311    304    304    304
##   [17,]    300    307    312    319    330    339    322    304    304
##   [18,]    304    310    319    327    343    365    354    324    304
##   [19,]    304    309    317    326    343    358    365    344    320
##   [20,]    294    300    308    319    338    362    364    359    328
##   [21,]    263    277    291    304    326    348    365    365    334
##   [22,]    243    259    274    290    312    334    349    365    332
##   [23,]    236    241    251    266    291    312    327    323    321
##   [24,]    227    234    239    243    275    293    304    310    309
##   [25,]    219    227    235    243    261    278    289    299    305
##   [26,]    210    220    229    236    248    263    274    283    292
##   [27,]    202    211    220    228    238    248    258    265    273
##   [28,]    196    204    212    221    232    240    243    248    251
##   [29,]    190    197    205    215    229    239    243    243    244
##   [30,]    182    190    199    213    231    239    243    243    243
##   [31,]    182    182    188    215    240    242    243    243    243
##   [32,]    174    180    182    212    243    242    243    242    243
##   [33,]    170    177    182    210    243    243    243    243    243
##   [34,]    165    174    182    202    233    243    243    243    243
##   [35,]    162    171    182    192    217    243    243    243    217
##   [36,]    159    167    174    180    197    220    228    216    203
##   [37,]    155    163    169    175    181    197    198    197    194
##   [38,]    149    157    164    171    179    182    185    187    186
##   [39,]    146    154    162    170    180    181    182    182    183
##   [40,]    144    152    161    170    181    182    182    182    182
##   [41,]    139    147    156    166    179    182    182    182    182
##   [42,]    133    141    153    169    182    182    182    165    131
##   [43,]    121    132    149    170    182    182    157    142    121
##   [44,]    118    121    148    175    180    182    150    121    130
##   [45,]    115    121    151    178    182    169    145    121    121
##   [46,]    114    121    162    182    182    148    121    129    121
##   [47,]    115    121    182    179    182    131    126    121    121
##   [48,]    121    149    182    182    182    121    122    121    121
##   [49,]    121    145    170    172    121    131    124    122    121
##   [50,]    121    133    144    129    123    120    120    122    121
##   [51,]    119    120    123    124    118    119    120    121    121
##   [52,]    103    121    121    116    113    118    120    121    121
##   [53,]     76     83     91     79    103    117    121    121    121
##   [54,]     60     60     62     63     73    118    121    121    121
##   [55,]     60     60     60     61    121    109    120    121    121
##   [56,]     60     60     60     75     99    115    121    121    121
##   [57,]     59     60     60     74    101    109    113    121    121
##   [58,]     58     60     60     73     96    103    109    112    117
##   [59,]     58     60     60     72     91     98    103    107    111
##   [60,]     60     60     60     70     85     91     97    101    106
##   [61,]     60     60     60     67     79     85     91     96    101
##   [62,]     60     60     60     66     73     80     85     91     97
##   [63,]     60     60     60     65     71     76     82     88     94
##   [64,]     60     60     60     63     70     75     80     86     92
##   [65,]     45     40     38     50     63     69     75     81     88
##   [66,]     14     14     15     29     47     60     67     74     80
##   [67,]      0      0      0      7     23     38     53     64     71
##   [68,]      0      0      0      0      0     15     33     48     60
##   [69,]      0      0      0      0      0      0     17     31     44
##   [70,]      0      0      0      0      0      0      7     14     21
##   [71,]      0      0      0      0      0      0      0      0      0
##   [72,]      0      0      0      0      0      0      0      0      0
##   [73,]      0      0      0      0      0      0      0      0      0
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##   [82,]      0      0      0      0      0      0      0      0      0
##   [83,]      0      0      0      0      0      0      0      0      0
##         [,272] [,273] [,274] [,275] [,276] [,277] [,278] [,279] [,280]
##    [1,]    259    249    236    226    215    202    188    170    157
##    [2,]    259    254    247    235    222    208    195    183    163
##    [3,]    280    265    252    238    222    205    193    182    162
##    [4,]    302    281    262    241    218    200    189    182    167
##    [5,]    317    297    271    243    213    199    189    184    176
##    [6,]    330    312    279    254    231    207    193    188    183
##    [7,]    342    322    298    274    254    234    213    198    187
##    [8,]    354    328    305    285    268    255    233    210    190
##    [9,]    363    351    326    299    273    253    224    202    178
##   [10,]    365    353    330    309    287    265    238    208    180
##   [11,]    365    352    335    319    300    272    248    214    188
##   [12,]    365    357    337    318    309    304    263    243    196
##   [13,]    349    344    330    316    304    265    243    234    198
##   [14,]    331    327    320    308    295    259    245    233    210
##   [15,]    313    313    311    304    292    277    264    243    226
##   [16,]    304    304    306    306    305    297    282    272    247
##   [17,]    304    302    304    304    304    304    304    304    275
##   [18,]    304    295    297    304    304    304    304    304    299
##   [19,]    304    285    280    295    304    304    304    304    304
##   [20,]    304    269    259    279    292    304    304    304    304
##   [21,]    304    243    247    263    278    292    304    304    304
##   [22,]    304    243    243    252    266    282    293    300    304
##   [23,]    304    243    243    243    249    269    286    298    304
##   [24,]    304    284    243    243    243    264    285    304    305
##   [25,]    305    284    243    243    243    266    289    304    306
##   [26,]    304    258    243    243    243    272    304    298    304
##   [27,]    266    252    243    243    243    264    277    293    299
##   [28,]    253    246    242    242    243    253    259    269    283
##   [29,]    245    243    239    238    241    243    243    250    273
##   [30,]    243    241    232    234    238    241    242    243    266
##   [31,]    243    237    220    227    238    242    243    263    297
##   [32,]    243    223    182    213    243    243    273    304    302
##   [33,]    243    192    189    182    243    246    271    288    304
##   [34,]    226    184    184    182    243    249    267    284    301
##   [35,]    202    183    182    182    213    243    268    287    303
##   [36,]    182    185    183    182    213    243    270    298    303
##   [37,]    182    181    183    182    213    243    274    294    304
##   [38,]    182    179    181    182    213    243    274    304    303
##   [39,]    182    172    178    182    213    243    274    304    304
##   [40,]    162    147    172    182    213    243    273    304    304
##   [41,]    121    125    160    182    213    243    272    304    304
##   [42,]    126    122    152    182    212    243    269    304    304
##   [43,]    122    123    152    182    211    234    251    270    290
##   [44,]    122    121    155    182    206    219    230    243    258
##   [45,]    123    135    172    183    199    208    216    223    239
##   [46,]    121    145    165    182    190    195    200    203    207
##   [47,]    121    140    158    169    182    184    186    184    182
##   [48,]    121    134    145    157    171    182    182    182    182
##   [49,]    121    125    128    140    164    177    180    181    182
##   [50,]    121    121    121    121    160    179    180    181    182
##   [51,]    121    121    134    156    172    184    187    182    182
##   [52,]    121    131    154    182    178    198    212    223    182
##   [53,]    121    131    158    167    182    191    208    233    243
##   [54,]    121    130    153    164    171    179    189    212    235
##   [55,]    121    128    146    157    164    170    176    190    213
##   [56,]    121    125    137    150    157    163    168    176    190
##   [57,]    121    121    128    143    149    154    159    166    175
##   [58,]    119    120    121    136    142    146    149    155    162
##   [59,]    114    118    121    130    134    137    139    143    148
##   [60,]    110    116    121    124    126    128    129    132    133
##   [61,]    106    113    119    121    121    122    123    124    124
##   [62,]    105    113    118    121    121    121    121    121    121
##   [63,]    103    112    118    121    121    121    121    121    121
##   [64,]    102    113    121    120    121    121    121    121    121
##   [65,]     98    109    117    121    121    121    121    121    121
##   [66,]     90    100    106    113    121    121    121    121    121
##   [67,]     81     90     95    102    112    121    121    121    121
##   [68,]     70     76     80     85    100    121    121    121    121
##   [69,]     56     50     50     56     71     91    111    118    116
##   [70,]     22     20     20     33     47     60     81     93    104
##   [71,]      0      0      0      8     23     38     53     73     92
##   [72,]      0      0      0      0      0     15     30     53     78
##   [73,]      0      0      0      0      0      0      7     34     55
##   [74,]      0      0      0      0      0      0      0     16     42
##   [75,]      0      0      0      0      0      0      0      6     32
##   [76,]      0      0      0      0      0      0      0      0     15
##   [77,]      0      0      0      0      0      0      0      0      0
##   [78,]      0      0      0      0      0      0      0      0      0
##   [79,]      0      0      0      0      0      0      0      0      0
##   [80,]      0      0      0      0      0      0      0      0      0
##   [81,]      0      0      0      0      0      0      0      0      0
##   [82,]      0      0      0      0      0      0      0      0      0
##   [83,]      0      0      0      0      0      0      0      0      0
##         [,281] [,282] [,283] [,284] [,285] [,286] [,287] [,288] [,289]
##    [1,]    145    130    118    109    101     95     89     86     83
##    [2,]    147    135    126    118    111    105     98     95     94
##    [3,]    145    134    126    120    115    108    101     98     97
##    [4,]    145    134    127    122    117    110    104    101     99
##    [5,]    159    142    130    123    118    112    107    103    102
##    [6,]    167    145    132    123    118    114    109    106    104
##    [7,]    169    146    132    124    120    116    112    109    107
##    [8,]    166    143    131    124    123    120    115    111    109
##    [9,]    150    138    130    130    131    126    119    114    112
##   [10,]    159    141    137    142    143    134    124    118    115
##   [11,]    168    157    152    159    159    143    130    120    117
##   [12,]    176    170    171    177    181    171    123    119    119
##   [13,]    182    182    182    180    182    121    128    121    121
##   [14,]    182    186    184    182    157    132    122    134    149
##   [15,]    224    200    192    182    170    154    152    162    182
##   [16,]    244    235    211    194    182    175    175    189    199
##   [17,]    250    243    227    208    182    182    182    208    224
##   [18,]    274    254    238    234    214    198    208    233    242
##   [19,]    304    284    271    253    243    235    238    239    250
##   [20,]    304    304    296    281    265    251    242    253    258
##   [21,]    304    305    305    304    289    278    276    271    268
##   [22,]    304    306    307    304    304    298    300    304    281
##   [23,]    309    313    317    318    317    320    322    311    305
##   [24,]    316    322    331    340    352    365    356    320    308
##   [25,]    315    321    333    347    365    363    358    311    306
##   [26,]    306    304    322    340    365    365    354    329    304
##   [27,]    302    304    304    314    342    359    362    355    353
##   [28,]    297    301    304    304    329    344    360    365    365
##   [29,]    295    303    304    315    323    336    353    362    365
##   [30,]    297    301    304    304    313    329    347    355    361
##   [31,]    303    303    303    304    304    322    343    352    358
##   [32,]    306    317    314    314    314    323    341    350    356
##   [33,]    311    330    343    345    345    349    349    354    358
##   [34,]    310    356    363    365    365    364    361    361    362
##   [35,]    333    365    365    364    365    365    365    364    364
##   [36,]    328    342    357    365    365    365    365    365    365
##   [37,]    320    330    338    342    345    350    365    365    365
##   [38,]    308    313    318    319    314    322    349    359    361
##   [39,]    304    304    305    304    305    304    334    344    348
##   [40,]    304    304    300    300    301    312    327    334    337
##   [41,]    304    292    292    288    293    308    319    325    326
##   [42,]    304    284    276    270    278    298    312    318    319
##   [43,]    278    267    250    245    252    280    298    308    308
##   [44,]    258    253    243    243    243    264    278    284    297
##   [45,]    246    238    241    242    243    250    256    256    275
##   [46,]    204    225    229    238    243    243    243    245    243
##   [47,]    182    191    210    230    243    243    243    243    264
##   [48,]    182    182    182    220    243    243    243    243    264
##   [49,]    182    182    201    218    243    243    243    243    266
##   [50,]    182    182    199    216    228    243    243    243    274
##   [51,]    182    182    192    205    217    233    243    262    277
##   [52,]    182    182    182    192    205    226    243    258    274
##   [53,]    202    182    182    182    195    222    243    258    273
##   [54,]    243    226    190    182    190    218    243    258    273
##   [55,]    219    198    199    192    200    220    243    257    270
##   [56,]    195    185    185    193    203    219    243    252    263
##   [57,]    182    180    182    189    199    211    229    243    252
##   [58,]    160    163    170    178    187    195    213    226    238
##   [59,]    146    145    153    161    166    180    196    210    225
##   [60,]    132    128    137    141    149    168    180    190    205
##   [61,]    121    123    121    121    132    159    173    178    182
##   [62,]    122    121    121    121    121    153    168    174    178
##   [63,]    121    121    121    121    121    148    164    170    175
##   [64,]    121    121    121    121    142    158    166    171    175
##   [65,]    121    121    121    134    170    176    177    175    176
##   [66,]    121    121    121    155    179    182    182    182    180
##   [67,]    121    121    148    172    181    181    182    182    182
##   [68,]    121    121    149    182    182    182    182    182    182
##   [69,]    119    121    138    158    178    182    182    182    182
##   [70,]    112    118    121    145    162    182    182    182    168
##   [71,]    104    116    121    134    143    155    162    150    152
##   [72,]     96    121    120    121    121    121    121    121    137
##   [73,]     70     94    108    105    106    111    115    119    121
##   [74,]     60     72     82     85     92    102    109    118    120
##   [75,]     46     60     71     74     83     96    106    121    121
##   [76,]     29     41     54     62     63     80     91    103    115
##   [77,]     11     24     36     39     49     60     73     85     93
##   [78,]      0      5     17     23     30     41     54     67     69
##   [79,]      0      0      0      8     12     17     31     36     39
##   [80,]      0      0      0      0      0      0      7      9      9
##   [81,]      0      0      0      0      0      0      0      0      0
##   [82,]      0      0      0      0      0      0      0      0      0
##   [83,]      0      0      0      0      0      0      0      0      0
##         [,290] [,291] [,292] [,293] [,294] [,295] [,296] [,297] [,298]
##    [1,]     81     82     79     79     85     90     96     99    100
##    [2,]     93     91     88     87     89     94     99    101    101
##    [3,]     96     94     91     90     92     96    100    101    102
##    [4,]     98     95     93     93     95     99    101    102    103
##    [5,]    101     98     96     96     98    102    103    104    105
##    [6,]    103    100     99     99    101    104    105    106    107
##    [7,]    106    103    102    101    103    106    107    108    110
##    [8,]    109    106    105    104    105    107    109    110    112
##    [9,]    112    109    108    107    108    110    111    112    113
##   [10,]    114    112    110    110    111    112    113    114    115
##   [11,]    116    114    113    112    113    114    115    115    116
##   [12,]    119    116    115    115    116    116    117    117    117
##   [13,]    121    119    118    118    119    118    118    119    119
##   [14,]    145    130    121    124    121    120    120    120    120
##   [15,]    182    160    156    155    137    121    121    121    121
##   [16,]    200    199    193    190    171    165    140    132    126
##   [17,]    231    243    225    217    202    188    182    165    149
##   [18,]    245    243    243    239    223    204    189    183    174
##   [19,]    249    248    245    244    243    214    191    182    168
##   [20,]    254    249    246    244    243    213    182    182    175
##   [21,]    261    251    246    244    227    214    207    196    188
##   [22,]    267    249    243    243    231    222    218    214    209
##   [23,]    290    255    244    243    240    235    233    232    234
##   [24,]    304    282    271    259    243    243    243    243    260
##   [25,]    299    295    296    290    283    294    301    292    292
##   [26,]    304    304    316    308    304    306    305    302    304
##   [27,]    350    341    338    332    318    311    306    304    304
##   [28,]    365    365    360    355    329    316    304    305    288
##   [29,]    365    365    365    363    343    327    311    304    299
##   [30,]    365    365    365    365    356    342    328    320    312
##   [31,]    363    365    365    365    365    353    338    328    320
##   [32,]    361    364    365    365    365    365    353    341    329
##   [33,]    362    363    364    365    365    365    365    355    342
##   [34,]    363    364    364    365    365    365    366    366    359
##   [35,]    364    364    364    364    365    365    367    368    368
##   [36,]    365    365    364    364    365    365    369    373    375
##   [37,]    365    365    364    364    365    365    372    378    384
##   [38,]    360    360    360    362    364    367    374    383    392
##   [39,]    349    351    354    358    362    364    365    376    387
##   [40,]    340    344    348    355    361    365    365    365    371
##   [41,]    332    338    343    352    360    365    365    365    365
##   [42,]    326    332    339    349    358    365    365    365    365
##   [43,]    315    323    331    343    354    360    365    365    365
##   [44,]    304    314    324    338    351    359    365    365    365
##   [45,]    297    307    318    334    349    357    364    365    365
##   [46,]    282    304    315    332    348    357    363    364    365
##   [47,]    281    304    316    335    349    357    365    365    365
##   [48,]    285    304    329    350    354    359    365    365    365
##   [49,]    289    304    345    365    362    362    364    365    365
##   [50,]    304    316    351    365    365    365    359    359    365
##   [51,]    297    310    352    365    365    365    351    342    326
##   [52,]    291    304    340    365    360    350    345    331    319
##   [53,]    289    304    335    349    355    347    338    329    317
##   [54,]    288    304    327    342    346    344    336    326    315
##   [55,]    285    304    318    335    339    349    340    327    315
##   [56,]    276    287    305    326    343    365    357    331    312
##   [57,]    263    275    290    304    324    343    365    330    303
##   [58,]    248    262    277    292    301    314    315    318    308
##   [59,]    243    249    265    281    292    304    304    307    307
##   [60,]    220    235    252    268    279    289    299    304    305
##   [61,]    197    213    236    253    264    275    286    296    304
##   [62,]    181    190    217    238    249    260    278    291    304
##   [63,]    179    182    201    224    235    243    262    277    290
##   [64,]    178    180    192    216    227    237    243    262    275
##   [65,]    178    180    187    206    220    232    243    247    254
##   [66,]    180    181    185    201    214    227    237    243    243
##   [67,]    182    182    182    197    211    226    236    243    245
##   [68,]    182    182    182    199    215    233    243    243    248
##   [69,]    181    180    182    198    217    236    242    248    253
##   [70,]    174    176    181    191    209    226    243    248    253
##   [71,]    160    167    177    182    201    215    225    234    238
##   [72,]    146    159    176    188    195    203    210    211    217
##   [73,]    135    150    166    182    190    195    199    197    203
##   [74,]    121    138    152    164    174    184    184    181    185
##   [75,]    126    129    137    143    145    148    158    170    182
##   [76,]    121    122    124    124    117    115    119    133    170
##   [77,]     97    103    116     97     99     98    104    112    126
##   [78,]     70     76     75     71     78     79     87     94    107
##   [79,]     48     60     55     53     60     60     71     74     85
##   [80,]     12     26     24     30     29     42     49     54     67
##   [81,]      0      0      0      5      0     16     18     24     42
##   [82,]      0      0      0      0      0      0      0      0     10
##   [83,]      0      0      0      0      0      0      0      0      0
##         [,299] [,300] [,301] [,302] [,303] [,304] [,305] [,306] [,307]
##    [1,]    103    111    119    122    123    124    125    128    143
##    [2,]    103    111    119    123    125    124    123    122    141
##    [3,]    105    111    119    126    129    126    123    122    141
##    [4,]    106    111    118    125    128    127    124    122    127
##    [5,]    108    112    116    120    124    124    123    122    125
##    [6,]    110    113    116    118    121    122    122    121    127
##    [7,]    111    114    117    119    121    121    121    121    128
##    [8,]    113    115    117    119    121    121    121    122    128
##    [9,]    114    116    118    119    121    121    121    122    129
##   [10,]    116    117    119    120    121    121    121    122    128
##   [11,]    117    118    119    120    121    121    121    121    127
##   [12,]    118    119    119    120    120    121    121    121    125
##   [13,]    119    119    120    120    121    121    121    121    124
##   [14,]    120    120    120    121    121    121    121    121    121
##   [15,]    121    121    121    121    121    121    121    121    121
##   [16,]    121    121    121    121    121    121    121    121    121
##   [17,]    137    124    121    121    121    121    121    121    121
##   [18,]    152    139    131    125    121    121    121    121    121
##   [19,]    163    151    145    138    129    121    121    121    121
##   [20,]    167    159    154    146    138    130    121    121    121
##   [21,]    178    170    168    160    151    143    134    123    121
##   [22,]    198    182    182    174    165    156    146    133    121
##   [23,]    231    215    201    188    178    169    157    143    131
##   [24,]    255    243    227    208    192    182    168    153    139
##   [25,]    291    267    243    227    208    188    179    163    147
##   [26,]    304    304    257    243    227    200    182    172    155
##   [27,]    297    267    251    246    232    203    185    173    155
##   [28,]    277    246    244    225    212    182    186    169    156
##   [29,]    295    274    244    232    214    203    190    178    173
##   [30,]    308    304    253    243    225    217    210    205    194
##   [31,]    311    305    243    239    233    228    226    224    218
##   [32,]    317    296    275    254    242    242    253    255    246
##   [33,]    323    304    289    274    272    275    284    292    263
##   [34,]    339    320    304    296    295    299    306    303    293
##   [35,]    358    343    331    304    304    320    313    307    304
##   [36,]    374    373    372    365    353    339    319    307    290
##   [37,]    393    396    391    365    365    365    318    291    263
##   [38,]    411    425    412    365    358    330    309    277    245
##   [39,]    402    426    405    365    341    320    304    262    243
##   [40,]    380    389    396    371    339    304    306    281    260
##   [41,]    365    367    369    365    353    331    304    302    304
##   [42,]    365    365    366    366    365    347    324    304    305
##   [43,]    365    365    365    365    365    365    352    328    314
##   [44,]    365    365    365    365    365    365    365    365    341
##   [45,]    365    364    364    365    365    365    365    365    365
##   [46,]    365    364    364    364    365    365    365    365    365
##   [47,]    360    360    361    363    365    365    365    365    365
##   [48,]    350    352    356    359    363    365    365    365    365
##   [49,]    337    340    347    354    362    365    365    365    365
##   [50,]    314    323    335    348    365    364    365    365    365
##   [51,]    303    301    312    327    343    365    365    364    365
##   [52,]    296    282    293    304    323    347    363    359    361
##   [53,]    291    264    276    291    304    324    341    352    357
##   [54,]    279    247    251    267    283    298    318    336    344
##   [55,]    291    243    246    243    262    283    307    320    330
##   [56,]    298    243    244    244    243    262    290    308    317
##   [57,]    261    266    247    244    243    243    274    292    304
##   [58,]    269    243    246    243    240    243    261    276    285
##   [59,]    284    243    238    232    228    236    248    259    264
##   [60,]    274    242    226    211    198    216    238    245    246
##   [61,]    304    243    210    182    188    182    213    243    243
##   [62,]    304    243    214    182    182    184    193    223    243
##   [63,]    304    243    219    182    182    182    182    192    189
##   [64,]    296    263    243    182    182    182    182    182    182
##   [65,]    259    243    226    195    182    182    182    182    182
##   [66,]    246    248    243    218    199    182    182    182    182
##   [67,]    247    249    247    237    212    182    182    182    182
##   [68,]    252    257    259    257    243    215    182    182    182
##   [69,]    261    269    278    291    272    256    211    182    182
##   [70,]    263    273    285    304    304    304    233    182    182
##   [71,]    249    261    272    284    297    304    270    230    198
##   [72,]    228    243    255    267    276    274    254    252    243
##   [73,]    207    225    243    255    260    259    247    245    246
##   [74,]    183    193    213    227    228    233    237    244    243
##   [75,]    182    178    182    189    182    200    214    231    243
##   [76,]    162    159    163    166    163    176    190    206    223
##   [77,]    121    130    134    132    121    150    170    182    203
##   [78,]    113    118    123    118    119    127    154    182    187
##   [79,]     93    103    103    106    109    115    131    154    182
##   [80,]     76     86     89     92     96    101    113    120    133
##   [81,]     60     71     76     80     83     87    100    113    121
##   [82,]     32     47     64     66     68     69     86    102    115
##   [83,]      0      0     23     38     44     53     67     85     97
##         [,308] [,309] [,310] [,311] [,312] [,313] [,314] [,315] [,316]
##    [1,]    158    168    175    182    188    192    209    222    226
##    [2,]    157    168    176    183    190    195    210    223    232
##    [3,]    156    166    175    183    189    195    210    223    232
##    [4,]    141    157    170    179    185    193    206    218    228
##    [5,]    136    150    165    176    182    189    199    211    221
##    [6,]    138    151    163    174    180    185    193    203    213
##    [7,]    138    150    161    171    178    182    189    196    203
##    [8,]    138    148    159    169    177    182    186    189    192
##    [9,]    139    149    159    170    177    181    183    184    185
##   [10,]    138    149    159    169    177    181    182    182    182
##   [11,]    137    147    158    169    176    180    182    182    182
##   [12,]    137    146    157    169    178    181    182    182    182
##   [13,]    136    147    159    174    182    181    182    182    182
##   [14,]    127    140    156    175    181    182    182    182    182
##   [15,]    121    121    139    158    182    182    182    182    182
##   [16,]    121    121    121    131    157    172    176    180    181
##   [17,]    121    121    121    131    141    155    171    178    180
##   [18,]    121    121    121    121    127    146    171    180    182
##   [19,]    121    121    121    121    121    134    182    180    182
##   [20,]    121    121    121    121    121    121    155    182    182
##   [21,]    121    121    121    121    121    121    129    154    174
##   [22,]    121    121    121    121    121    121    121    133    153
##   [23,]    124    121    121    121    121    121    121    121    137
##   [24,]    132    126    121    121    121    121    121    121    121
##   [25,]    138    130    125    122    121    121    121    121    121
##   [26,]    144    133    127    124    121    121    121    121    121
##   [27,]    141    126    125    123    122    121    121    121    121
##   [28,]    140    121    121    122    121    121    121    121    121
##   [29,]    154    131    121    121    121    121    121    121    121
##   [30,]    182    155    121    121    121    121    121    121    121
##   [31,]    197    182    144    121    121    121    121    121    121
##   [32,]    229    182    162    134    121    121    121    121    121
##   [33,]    243    223    182    163    144    121    121    121    121
##   [34,]    269    243    220    191    172    135    121    121    121
##   [35,]    304    261    243    204    188    162    121    121    121
##   [36,]    269    253    226    192    177    153    121    121    121
##   [37,]    243    209    182    188    173    149    134    121    121
##   [38,]    226    199    186    182    179    156    138    124    121
##   [39,]    243    228    205    185    175    160    141    121    124
##   [40,]    250    243    216    182    176    157    144    121    121
##   [41,]    275    243    231    212    187    167    158    150    139
##   [42,]    304    243    243    239    225    182    179    182    182
##   [43,]    304    264    243    251    242    227    207    228    208
##   [44,]    323    304    288    276    271    263    243    246    243
##   [45,]    354    328    312    301    299    305    294    274    254
##   [46,]    365    347    333    332    335    320    308    304    271
##   [47,]    365    360    354    359    362    340    318    304    281
##   [48,]    365    365    365    364    365    345    324    304    281
##   [49,]    365    365    365    365    365    346    325    304    274
##   [50,]    365    365    365    365    365    348    325    304    263
##   [51,]    365    365    365    365    365    353    324    304    243
##   [52,]    364    365    365    365    365    351    312    299    259
##   [53,]    365    365    365    365    365    344    322    304    280
##   [54,]    352    361    365    365    365    359    327    309    298
##   [55,]    339    348    356    365    365    365    327    315    309
##   [56,]    326    335    343    351    358    335    320    313    309
##   [57,]    313    322    330    337    342    326    316    311    308
##   [58,]    296    309    317    321    329    321    315    311    309
##   [59,]    267    285    304    304    316    318    315    312    309
##   [60,]    241    254    268    279    302    310    310    310    309
##   [61,]    223    221    243    243    275    304    306    306    306
##   [62,]    202    182    207    230    254    290    304    305    305
##   [63,]    184    186    183    193    235    277    304    304    304
##   [64,]    182    183    182    205    231    272    304    304    304
##   [65,]    182    182    182    208    241    265    280    297    304
##   [66,]    182    182    192    205    232    254    266    279    290
##   [67,]    182    182    182    189    214    241    249    261    268
##   [68,]    182    182    182    182    199    243    242    243    243
##   [69,]    182    182    182    182    199    213    223    215    225
##   [70,]    182    182    182    182    182    186    182    182    199
##   [71,]    182    182    182    181    179    180    181    182    182
##   [72,]    213    182    182    180    173    175    178    181    182
##   [73,]    243    213    182    179    168    170    175    182    189
##   [74,]    244    243    228    171    137    151    163    177    188
##   [75,]    243    243    211    167    121    121    142    163    182
##   [76,]    229    216    203    167    121    121    121    147    172
##   [77,]    201    199    195    167    121    121    121    142    182
##   [78,]    190    190    188    169    130    121    121    121    145
##   [79,]    182    184    184    173    143    121    121    121    121
##   [80,]    165    182    182    177    155    137    121    121    121
##   [81,]    142    163    182    182    169    145    131    121    121
##   [82,]    127    142    153    170    168    149    133    123    121
##   [83,]    109    121    121    139    138    134    130    121    117
##         [,317] [,318] [,319] [,320] [,321] [,322] [,323] [,324] [,325]
##    [1,]    234    250    265    279    291    304    306    305    326
##    [2,]    238    251    266    279    291    304    307    306    327
##    [3,]    238    251    266    279    291    304    304    308    327
##    [4,]    236    245    257    270    277    285    291    304    310
##    [5,]    231    240    249    256    263    267    273    284    293
##    [6,]    220    229    237    243    249    252    256    267    276
##    [7,]    208    215    223    232    237    241    244    254    264
##    [8,]    196    201    210    221    231    237    242    248    260
##    [9,]    186    190    200    214    227    237    242    247    261
##   [10,]    182    185    195    211    227    237    242    246    257
##   [11,]    182    185    195    211    227    236    242    244    250
##   [12,]    182    182    190    200    217    233    243    243    241
##   [13,]    182    182    182    182    198    205    216    228    234
##   [14,]    182    182    182    182    182    182    191    216    225
##   [15,]    182    182    182    182    182    182    202    210    220
##   [16,]    182    182    182    182    182    185    196    207    215
##   [17,]    181    182    182    182    182    188    195    203    212
##   [18,]    182    182    182    182    182    188    194    200    204
##   [19,]    182    182    182    182    182    182    184    186    182
##   [20,]    182    182    182    182    182    182    182    182    183
##   [21,]    182    182    182    181    180    181    182    182    182
##   [22,]    168    182    176    173    176    179    181    182    182
##   [23,]    150    155    155    164    170    177    181    182    182
##   [24,]    133    135    139    153    164    174    180    182    182
##   [25,]    121    121    124    143    161    179    182    182    182
##   [26,]    121    121    121    121    153    182    182    182    182
##   [27,]    121    121    121    121    129    149    169    179    182
##   [28,]    121    121    121    121    121    121    141    162    182
##   [29,]    121    121    121    121    121    121    121    148    166
##   [30,]    121    121    121    121    121    121    121    127    148
##   [31,]    121    121    121    121    121    121    121    121    131
##   [32,]    121    121    121    121    121    121    121    121    121
##   [33,]    121    121    121    121    121    121    121    121    121
##   [34,]    121    121    121    121    121    121    121    121    121
##   [35,]    121    121    121    121    121    121    121    121    121
##   [36,]    121    121    121    121    121    121    121    121    121
##   [37,]    121    121    121    121    121    121    121    121    121
##   [38,]    121    121    121    121    121    121    121    121    121
##   [39,]    122    121    121    121    121    121    121    121    121
##   [40,]    122    122    121    121    121    121    121    121    121
##   [41,]    128    122    121    121    121    121    121    121    121
##   [42,]    161    139    121    121    121    121    121    121    121
##   [43,]    190    172    138    121    121    121    121    121    121
##   [44,]    215    182    162    137    121    121    121    121    121
##   [45,]    243    218    184    160    142    127    121    121    121
##   [46,]    254    243    211    182    160    141    121    121    121
##   [47,]    260    245    223    187    177    160    136    121    121
##   [48,]    259    249    224    189    185    182    143    130    121
##   [49,]    250    234    201    184    178    159    139    127    123
##   [50,]    243    213    184    178    169    154    133    121    121
##   [51,]    235    215    182    175    168    151    121    124    121
##   [52,]    238    224    200    182    186    173    154    134    124
##   [53,]    265    243    223    223    202    191    182    160    142
##   [54,]    283    265    241    247    233    213    192    177    166
##   [55,]    304    304    285    274    259    243    223    210    187
##   [56,]    307    305    304    304    293    272    252    235    211
##   [57,]    307    305    304    304    304    304    277    261    234
##   [58,]    307    306    305    304    304    304    298    290    265
##   [59,]    308    306    305    304    304    304    304    304    304
##   [60,]    307    305    304    304    304    304    304    304    304
##   [61,]    306    305    304    304    304    304    304    304    304
##   [62,]    305    305    304    304    304    304    304    304    304
##   [63,]    304    304    304    303    304    304    304    304    304
##   [64,]    304    304    303    301    301    304    304    304    303
##   [65,]    304    304    299    295    291    296    304    304    300
##   [66,]    304    304    289    279    270    278    291    304    282
##   [67,]    282    283    267    251    246    252    267    266    257
##   [68,]    259    257    255    243    243    243    243    249    242
##   [69,]    235    244    247    243    243    234    227    224    212
##   [70,]    216    238    246    248    243    223    199    182    182
##   [71,]    192    234    254    265    255    233    199    185    182
##   [72,]    204    231    273    304    304    258    243    182    182
##   [73,]    207    237    273    304    304    263    243    182    182
##   [74,]    213    249    270    293    294    254    238    197    182
##   [75,]    198    233    257    272    264    266    243    200    182
##   [76,]    182    215    238    251    252    249    245    221    182
##   [77,]    185    202    226    243    243    245    245    230    182
##   [78,]    170    192    211    224    237    243    243    238    182
##   [79,]    140    173    194    206    219    231    243    243    216
##   [80,]    121    149    173    188    200    213    222    240    233
##   [81,]    121    129    144    163    182    194    199    221    243
##   [82,]    119    121    121    142    166    182    182    207    230
##   [83,]    117    119    120    121    148    162    174    190    212
##         [,326] [,327] [,328] [,329] [,330] [,331] [,332] [,333] [,334]
##    [1,]    344    355    367    379    389    395    395    391    380
##    [2,]    344    355    367    378    388    393    393    391    382
##    [3,]    342    353    365    375    386    389    391    389    382
##    [4,]    327    346    358    366    375    382    385    383    379
##    [5,]    305    321    338    353    363    373    378    378    375
##    [6,]    288    302    312    329    347    361    369    372    372
##    [7,]    277    290    301    317    333    350    360    366    369
##    [8,]    278    292    300    312    323    335    350    359    364
##    [9,]    282    294    300    308    317    323    334    349    356
##   [10,]    271    284    292    300    306    308    315    328    341
##   [11,]    261    271    279    291    291    289    295    307    321
##   [12,]    245    258    263    269    271    268    275    288    301
##   [13,]    239    243    243    243    243    243    257    275    294
##   [14,]    234    240    242    243    243    243    243    260    286
##   [15,]    231    238    241    242    243    243    243    253    283
##   [16,]    228    239    242    243    243    243    243    267    297
##   [17,]    229    243    242    243    243    243    243    266    288
##   [18,]    223    242    243    243    243    243    243    259    282
##   [19,]    203    234    239    240    241    242    243    246    272
##   [20,]    182    215    226    233    238    241    243    251    266
##   [21,]    192    210    220    229    238    242    243    250    269
##   [22,]    188    206    217    228    243    242    243    248    262
##   [23,]    186    198    206    216    231    243    243    245    249
##   [24,]    182    185    188    191    191    182    213    224    236
##   [25,]    182    182    183    183    182    184    183    202    214
##   [26,]    182    182    182    182    182    182    182    182    195
##   [27,]    182    182    181    181    181    181    182    182    191
##   [28,]    182    177    178    180    181    182    182    182    202
##   [29,]    177    174    177    179    181    182    182    182    200
##   [30,]    157    167    172    178    182    182    182    182    196
##   [31,]    144    157    166    174    182    182    182    182    189
##   [32,]    130    146    157    168    176    181    182    182    185
##   [33,]    121    137    150    162    174    178    182    182    186
##   [34,]    122    134    146    159    178    181    182    182    182
##   [35,]    121    129    142    151    159    171    177    181    182
##   [36,]    121    121    127    129    141    156    171    180    182
##   [37,]    121    121    121    121    121    145    169    182    182
##   [38,]    121    121    121    121    136    147    170    182    182
##   [39,]    121    121    121    121    136    149    165    175    182
##   [40,]    121    121    121    123    135    146    161    172    176
##   [41,]    121    121    121    125    133    142    155    166    172
##   [42,]    121    121    121    126    133    139    151    162    169
##   [43,]    121    121    121    128    134    140    150    160    167
##   [44,]    121    121    121    128    134    140    148    157    164
##   [45,]    121    121    121    126    132    137    144    152    156
##   [46,]    121    121    121    124    129    133    137    143    146
##   [47,]    121    121    121    121    123    125    127    131    133
##   [48,]    121    121    121    121    121    121    122    123    124
##   [49,]    121    121    121    121    121    121    121    121    121
##   [50,]    122    121    121    121    121    121    121    121    121
##   [51,]    121    121    121    121    121    121    121    121    121
##   [52,]    121    121    121    121    121    121    120    119    120
##   [53,]    121    121    121    121    120    119    118    115    112
##   [54,]    149    137    126    121    119    117    115    109    101
##   [55,]    170    157    143    131    121    121    121    109     94
##   [56,]    188    176    158    144    134    124    121    121    104
##   [57,]    202    182    171    155    141    124    121    121    121
##   [58,]    220    193    178    162    148    127    121    121    112
##   [59,]    243    218    182    173    167    158    135    121    121
##   [60,]    304    243    203    182    191    182    161    147    135
##   [61,]    283    277    243    243    219    192    183    174    152
##   [62,]    292    284    269    249    243    200    182    166    164
##   [63,]    304    304    285    265    243    208    183    173    157
##   [64,]    304    304    304    286    260    228    193    182    162
##   [65,]    300    304    304    304    269    231    187    180    169
##   [66,]    284    294    304    279    268    236    208    182    182
##   [67,]    263    275    278    267    255    248    234    219    201
##   [68,]    243    256    262    255    249    246    245    243    224
##   [69,]    224    237    248    249    247    245    243    243    243
##   [70,]    198    215    232    243    245    244    243    243    243
##   [71,]    182    201    222    243    243    243    243    233    217
##   [72,]    182    182    196    231    243    243    243    223    191
##   [73,]    181    181    182    203    226    243    243    243    182
##   [74,]    180    177    180    188    212    239    243    243    233
##   [75,]    176    168    172    182    194    222    243    243    243
##   [76,]    159    135    152    167    182    208    236    243    243
##   [77,]    153    121    121    142    164    192    217    228    243
##   [78,]    158    121    121    121    135    177    200    207    204
##   [79,]    182    150    121    121    121    136    182    182    182
##   [80,]    196    175    150    130    121    121    133    137    145
##   [81,]    223    182    170    153    138    121    121    121    121
##   [82,]    243    202    182    167    152    129    121    121    121
##   [83,]    195    194    189    184    175    152    135    134    131
##         [,335] [,336] [,337] [,338] [,339] [,340] [,341] [,342] [,343]
##    [1,]    371    365    352    329    314    300    281    271    259
##    [2,]    372    367    353    329    314    300    289    277    266
##    [3,]    374    369    354    337    322    307    295    283    269
##    [4,]    373    370    365    356    338    321    308    294    277
##    [5,]    372    370    368    365    351    331    318    305    285
##    [6,]    371    370    368    366    354    333    318    301    284
##    [7,]    369    369    367    366    353    329    312    297    277
##    [8,]    366    367    366    366    355    335    316    298    278
##    [9,]    360    364    365    366    360    346    332    318    301
##   [10,]    350    358    363    365    364    357    346    335    322
##   [11,]    336    350    359    364    365    364    358    351    340
##   [12,]    313    337    357    365    365    365    365    365    359
##   [13,]    304    316    338    355    365    365    365    365    365
##   [14,]    297    304    327    348    365    365    365    365    365
##   [15,]    297    304    326    345    365    365    365    365    365
##   [16,]    303    315    330    348    365    365    365    365    365
##   [17,]    304    312    334    354    365    365    365    365    365
##   [18,]    295    304    336    365    362    364    364    365    365
##   [19,]    290    304    327    344    361    364    364    365    365
##   [20,]    286    304    319    333    351    365    365    365    365
##   [21,]    282    298    308    321    340    359    365    365    365
##   [22,]    274    288    304    311    328    345    356    365    365
##   [23,]    260    273    285    298    314    332    344    356    365
##   [24,]    243    255    267    280    299    317    331    348    365
##   [25,]    229    240    249    261    287    303    311    336    348
##   [26,]    215    230    239    243    280    304    318    326    335
##   [27,]    209    229    241    251    285    303    313    317    320
##   [28,]    220    243    241    255    290    304    304    304    304
##   [29,]    218    229    243    243    271    304    290    292    299
##   [30,]    211    222    228    235    247    253    266    275    282
##   [31,]    203    212    219    225    235    243    243    259    265
##   [32,]    194    202    209    216    230    243    247    247    249
##   [33,]    190    192    196    201    222    243    243    243    243
##   [34,]    183    182    182    182    206    235    240    242    243
##   [35,]    182    182    182    182    204    222    234    242    243
##   [36,]    182    182    182    182    202    221    240    242    243
##   [37,]    182    182    182    182    198    212    226    243    243
##   [38,]    182    182    182    182    188    190    205    220    228
##   [39,]    182    182    182    182    182    183    182    207    219
##   [40,]    180    182    182    182    182    182    206    201    214
##   [41,]    178    182    182    182    182    182    201    208    211
##   [42,]    176    182    182    182    182    182    196    201    206
##   [43,]    174    182    182    182    182    182    189    193    196
##   [44,]    171    182    182    182    182    182    182    184    185
##   [45,]    161    167    176    182    182    182    182    182    183
##   [46,]    149    152    156    175    182    182    182    182    177
##   [47,]    134    133    131    147    157    159    159    158    167
##   [48,]    124    121    123    121    135    136    136    141    150
##   [49,]    122    121    121    122    121    121    121    131    140
##   [50,]    121    121    121    121    121    121    121    121    126
##   [51,]    121    121    121    121    121    121    120    120    121
##   [52,]    121    121    121    121    121    119    117    116    119
##   [53,]    113    121    121    121    121    114    109    106    108
##   [54,]     93     88     91    121    112    103     98     94     95
##   [55,]     79     60     65     72     89     86     84     82     81
##   [56,]     82     60     60     61     66     71     71     70     68
##   [57,]     92     78     60     60     60     60     62     63     60
##   [58,]    104     95     78     60     60     60     60     60     60
##   [59,]    121    121    101     71     60     60     60     60     60
##   [60,]    129    124    121     89     60     60     60     60     60
##   [61,]    140    131    124    108     74     60     60     60     60
##   [62,]    147    134    125    110     80     60     60     60     60
##   [63,]    143    126    121    103     78     60     60     60     60
##   [64,]    145    130    121    107     71     60     60     60     60
##   [65,]    150    125    122     95     60     61     60     60     60
##   [66,]    164    145    121     99     60     60     60     60     60
##   [67,]    187    172    146    118     60     60     60     60     60
##   [68,]    203    182    163    130     60     60     60     60     60
##   [69,]    230    182    165    133     81     60     60     60     60
##   [70,]    208    182    172    145    121     60     60     60     60
##   [71,]    198    192    182    153    121    101     60     60     60
##   [72,]    185    184    184    157    129    121     60     60     60
##   [73,]    182    178    150    121    121     94     60     60     60
##   [74,]    199    176    147    125    115     95     60     60     60
##   [75,]    243    214    170    142    127    121     60     60     60
##   [76,]    243    227    176    151    134    121     71     60     61
##   [77,]    217    207    178    154    137    121     60     68     62
##   [78,]    201    193    180    154    134    121     60     61     62
##   [79,]    182    182    158    139    121     60     86     64     61
##   [80,]    145    133    132    130    121     76     60     65     60
##   [81,]    121    124    121    121    100     94     81     60     60
##   [82,]    121    121    122    121    105     97     91     77     60
##   [83,]    121    121    121    121    117    115    113     98     89
##         [,344] [,345] [,346] [,347] [,348] [,349] [,350] [,351] [,352]
##    [1,]    239    214    188    172    158    140    122    112    110
##    [2,]    254    221    191    173    159    141    131    124    117
##    [3,]    256    222    192    174    159    141    131    125    119
##    [4,]    260    222    193    174    157    140    129    124    120
##    [5,]    266    227    196    176    159    141    133    125    123
##    [6,]    264    227    199    182    174    163    143    131    131
##    [7,]    260    232    208    194    192    183    173    157    142
##    [8,]    258    243    229    219    213    201    188    176    157
##    [9,]    286    268    255    244    235    216    199    182    162
##   [10,]    309    297    280    265    251    229    205    184    161
##   [11,]    327    314    300    280    261    224    202    181    157
##   [12,]    345    328    309    293    264    243    197    178    161
##   [13,]    365    339    312    277    243    231    210    182    167
##   [14,]    365    346    317    294    243    224    206    182    173
##   [15,]    365    349    321    304    243    227    211    199    182
##   [16,]    365    350    316    277    243    233    224    216    210
##   [17,]    365    365    319    284    243    243    240    236    234
##   [18,]    365    365    333    304    272    243    243    242    242
##   [19,]    365    365    349    316    297    276    258    258    261
##   [20,]    366    366    365    345    332    304    288    302    307
##   [21,]    366    367    367    368    367    350    335    349    350
##   [22,]    367    368    369    374    376    378    381    385    381
##   [23,]    368    370    372    382    389    397    405    416    415
##   [24,]    369    371    376    387    398    410    426    423    426
##   [25,]    357    361    367    382    396    411    426    426    426
##   [26,]    341    347    357    365    387    406    426    426    426
##   [27,]    327    336    348    361    371    391    416    426    426
##   [28,]    313    322    336    350    358    365    391    413    420
##   [29,]    304    319    333    343    353    365    377    382    398
##   [30,]    291    304    319    329    339    348    357    362    378
##   [31,]    275    291    304    314    324    331    338    347    361
##   [32,]    260    279    299    304    309    311    322    333    349
##   [33,]    243    270    304    304    304    301    304    316    336
##   [34,]    243    255    269    278    281    290    297    303    318
##   [35,]    243    245    243    256    265    278    289    299    304
##   [36,]    243    243    243    243    250    270    286    302    308
##   [37,]    240    242    243    243    257    264    279    291    304
##   [38,]    238    241    243    243    255    265    272    283    294
##   [39,]    230    240    243    243    251    256    259    269    281
##   [40,]    224    238    243    243    243    243    243    253    267
##   [41,]    217    227    236    238    236    230    234    240    249
##   [42,]    209    215    220    221    218    214    220    227    234
##   [43,]    196    202    206    206    204    198    205    213    218
##   [44,]    182    188    191    191    189    182    191    200    203
##   [45,]    182    183    184    185    185    182    182    187    188
##   [46,]    178    181    182    182    183    182    181    182    182
##   [47,]    172    179    182    182    182    181    180    181    182
##   [48,]    158    169    182    182    170    175    176    180    182
##   [49,]    148    159    165    161    162    167    172    178    182
##   [50,]    134    142    147    141    148    155    163    174    182
##   [51,]    121    126    127    121    133    143    153    169    182
##   [52,]    121    122    118    119    121    127    140    162    182
##   [53,]    109    108    110    113    116    120    121    152    173
##   [54,]     94     93    101    106    112    117    121    143    167
##   [55,]     78     78     90     98    106    114    121    139    160
##   [56,]     64     64     78     89     98    108    118    132    152
##   [57,]     62     60     66     77     88    100    111    127    143
##   [58,]     60     60     60     65     76     90    103    120    133
##   [59,]     60     60     60     60     60     78     92    108    121
##   [60,]     60     60     60     60     60     70     84    102    121
##   [61,]     60     60     60     60     60     63     75     90    105
##   [62,]     60     60     60     60     60     60     66     76     93
##   [63,]     60     60     60     60     60     60     60     63     82
##   [64,]     60     60     60     60     60     60     60     60     72
##   [65,]     60     60     60     60     60     60     60     60     68
##   [66,]     60     60     60     60     60     60     60     60     60
##   [67,]     60     60     60     60     60     60     60     60     60
##   [68,]     60     60     60     60     60     60     60     60     60
##   [69,]     60     60     60     60     60     60     60     60     60
##   [70,]     60     60     60     60     60     60     60     60     60
##   [71,]     60     60     60     60     60     60     60     60     60
##   [72,]     60     60     60     60     60     60     60     60     60
##   [73,]     60     60     60     60     60     60     60     60     60
##   [74,]     60     60     60     60     60     60     60     60     60
##   [75,]     60     60     60     61     60     60     60     60     60
##   [76,]     60     60     62     62     61     60     60     60     60
##   [77,]     61     60     66     67     60     60     60     60     60
##   [78,]     61     76     81     83     73     65     62     61     60
##   [79,]     81     97    103    106     86     74     67     62     61
##   [80,]     90    121    121    121     96     80     69     63     61
##   [81,]     88    121    121    121    102     83     66     62     61
##   [82,]     91     89    108    121     96     79     61     61     60
##   [83,]     65     60     72     77     80     73     60     61     60
##         [,353] [,354] [,355] [,356] [,357] [,358] [,359] [,360] [,361]
##    [1,]    110    115    146    173    180    182    212    243    263
##    [2,]    113    116    147    173    182    184    214    243    263
##    [3,]    114    117    147    173    187    191    217    245    264
##    [4,]    117    118    128    148    165    189    228    257    270
##    [5,]    121    120    122    134    147    178    234    273    286
##    [6,]    125    122    122    124    137    173    235    274    291
##    [7,]    131    125    124    126    142    174    236    275    291
##    [8,]    139    129    127    134    156    178    209    250    259
##    [9,]    141    130    126    127    135    158    189    217    225
##   [10,]    142    130    124    123    124    139    166    179    192
##   [11,]    139    129    124    122    121    129    143    155    161
##   [12,]    137    121    121    121    121    121    125    130    131
##   [13,]    150    136    121    121    121    121    121    121    121
##   [14,]    165    157    144    132    125    121    121    121    121
##   [15,]    182    182    167    156    145    133    121    121    121
##   [16,]    212    200    188    176    164    149    129    121    121
##   [17,]    243    227    209    195    182    174    161    131    121
##   [18,]    242    243    221    210    206    203    188    162    137
##   [19,]    252    243    238    232    234    233    218    182    159
##   [20,]    273    264    243    243    261    254    245    205    182
##   [21,]    298    309    306    288    292    274    250    222    207
##   [22,]    365    365    365    304    309    304    256    233    227
##   [23,]    412    397    384    372    345    304    278    254    249
##   [24,]    426    426    410    395    380    365    297    277    267
##   [25,]    426    426    426    418    403    385    353    297    282
##   [26,]    426    426    426    426    426    402    378    365    304
##   [27,]    426    426    426    426    426    412    382    365    335
##   [28,]    426    426    426    426    426    420    389    360    339
##   [29,]    416    426    426    426    426    426    416    387    365
##   [30,]    399    413    426    426    426    426    426    416    396
##   [31,]    380    398    413    426    426    426    426    426    426
##   [32,]    365    381    396    410    422    426    426    426    426
##   [33,]    355    365    381    396    411    426    426    426    426
##   [34,]    344    359    369    381    396    415    426    426    426
##   [35,]    328    344    356    365    382    403    426    426    426
##   [36,]    320    332    347    360    369    388    408    421    426
##   [37,]    313    323    335    346    356    372    393    405    426
##   [38,]    304    314    328    338    347    361    380    387    408
##   [39,]    295    304    316    325    334    348    359    363    379
##   [40,]    281    291    304    313    321    335    345    353    360
##   [41,]    262    268    282    297    309    322    335    343    352
##   [42,]    243    243    259    277    291    309    324    335    346
##   [43,]    229    237    243    259    273    294    310    326    339
##   [44,]    214    226    236    243    256    284    304    316    330
##   [45,]    199    215    228    239    243    281    304    311    319
##   [46,]    182    208    226    243    261    290    299    303    306
##   [47,]    190    205    225    243    262    288    304    303    303
##   [48,]    197    213    226    243    259    276    291    304    304
##   [49,]    197    213    228    243    255    268    279    283    279
##   [50,]    197    212    227    243    246    253    259    261    257
##   [51,]    196    211    226    243    243    244    246    246    243
##   [52,]    192    206    220    235    243    243    243    241    240
##   [53,]    182    197    206    214    218    229    232    235    238
##   [54,]    182    186    189    191    192    208    222    229    235
##   [55,]    171    182    179    181    182    191    212    223    233
##   [56,]    162    168    174    179    182    190    202    214    224
##   [57,]    153    162    170    179    182    189    192    202    208
##   [58,]    143    154    165    177    182    183    182    187    189
##   [59,]    131    141    153    163    167    171    177    179    182
##   [60,]    121    131    145    153    157    163    171    177    182
##   [61,]    114    121    133    139    143    149    159    171    182
##   [62,]    104    114    121    124    124    121    138    158    170
##   [63,]     94    106    116    121    121    121    127    144    154
##   [64,]     83     94    103    108    118    121    128    133    137
##   [65,]     73     82     91    100    111    121    121    122    123
##   [66,]     60     70     79     89    105    121    121    121    121
##   [67,]     60     60     65     75     94    108    115    118    120
##   [68,]     60     60     60     60     82     96    104    110    117
##   [69,]     60     60     60     66     75     88     98    106    114
##   [70,]     60     60     60     60     65     76     88     99    110
##   [71,]     60     60     60     60     60     60     77     89     99
##   [72,]     60     60     60     60     60     60     68     76     83
##   [73,]     60     60     60     60     60     60     60     63     66
##   [74,]     60     60     60     60     60     60     60     60     61
##   [75,]     60     60     60     60     60     60     60     59     59
##   [76,]     60     60     60     60     60     59     58     57     56
##   [77,]     60     60     60     60     60     58     57     55     54
##   [78,]     60     60     60     60     59     57     55     53     51
##   [79,]     60     60     60     60     59     56     53     51     48
##   [80,]     60     60     60     60     58     55     52     49     46
##   [81,]     60     60     60     60     58     53     50     46     43
##   [82,]     60     60     60     60     57     52     47     44     40
##   [83,]     60     60     60     60     56     50     45     41     37
##         [,362] [,363] [,364] [,365] [,366] [,367] [,368] [,369] [,370]
##    [1,]    275    282    265    249    218    202    198    191    189
##    [2,]    275    279    264    249    218    202    191    186    186
##    [3,]    276    271    257    240    211    196    188    184    184
##    [4,]    272    258    247    220    205    193    185    181    178
##    [5,]    283    265    240    213    196    188    181    176    172
##    [6,]    290    266    240    212    194    182    174    168    162
##    [7,]    283    262    237    210    190    178    167    158    151
##    [8,]    255    243    226    205    186    171    159    148    140
##    [9,]    218    211    197    184    170    158    147    139    132
##   [10,]    190    181    175    164    154    145    137    133    132
##   [11,]    159    154    151    145    138    133    131    133    136
##   [12,]    130    129    128    126    122    123    131    136    143
##   [13,]    121    121    121    121    121    127    138    156    168
##   [14,]    121    121    121    121    121    126    129    175    184
##   [15,]    121    121    121    121    121    121    182    173    192
##   [16,]    121    121    121    121    121    182    170    188    197
##   [17,]    121    121    121    121    126    170    182    192    204
##   [18,]    121    121    121    121    121    147    182    189    199
##   [19,]    133    121    121    121    121    129    148    171    187
##   [20,]    163    143    121    121    121    121    121    141    163
##   [21,]    192    172    152    126    121    121    121    121    140
##   [22,]    220    199    182    145    121    121    121    121    121
##   [23,]    245    229    198    164    131    121    121    121    121
##   [24,]    255    245    243    176    153    138    121    121    121
##   [25,]    268    251    236    208    175    160    144    129    121
##   [26,]    289    269    256    233    204    182    167    152    137
##   [27,]    304    280    266    249    223    201    182    167    152
##   [28,]    304    293    280    263    243    224    207    192    175
##   [29,]    337    304    294    281    259    243    228    221    202
##   [30,]    379    370    335    305    284    267    256    248    233
##   [31,]    410    392    377    335    310    291    286    270    253
##   [32,]    426    410    397    377    347    305    306    295    271
##   [33,]    426    426    414    393    373    365    316    304    292
##   [34,]    426    426    426    409    382    365    342    306    296
##   [35,]    426    426    426    421    395    378    365    304    288
##   [36,]    426    426    426    426    409    388    365    325    299
##   [37,]    426    426    426    426    426    408    388    365    338
##   [38,]    426    426    426    426    426    426    406    386    365
##   [39,]    407    420    426    426    426    426    426    416    396
##   [40,]    365    386    411    426    426    426    426    426    426
##   [41,]    360    365    389    418    426    426    426    426    426
##   [42,]    356    365    382    404    426    426    426    426    426
##   [43,]    351    365    375    389    405    419    426    426    426
##   [44,]    341    351    365    371    382    396    409    426    426
##   [45,]    326    333    335    347    360    373    377    397    416
##   [46,]    309    311    311    313    336    346    358    365    386
##   [47,]    305    305    294    301    312    326    345    357    365
##   [48,]    289    278    275    286    296    304    327    342    359
##   [49,]    275    261    261    275    286    296    304    323    345
##   [50,]    249    245    246    260    273    285    296    304    328
##   [51,]    244    243    243    243    262    275    288    296    304
##   [52,]    242    243    243    247    256    268    279    289    297
##   [53,]    240    242    243    251    259    265    274    282    291
##   [54,]    240    243    243    250    257    263    270    277    285
##   [55,]    243    243    243    249    254    260    266    273    279
##   [56,]    237    243    243    247    250    255    261    268    274
##   [57,]    219    232    243    243    243    249    256    263    269
##   [58,]    207    222    234    241    243    243    252    259    265
##   [59,]    188    209    225    239    243    245    249    254    260
##   [60,]    193    199    220    243    242    246    248    249    252
##   [61,]    190    199    209    224    233    236    238    239    240
##   [62,]    182    190    195    207    210    216    222    227    231
##   [63,]    162    172    178    188    189    199    209    216    227
##   [64,]    139    148    162    175    182    182    197    206    218
##   [65,]    122    128    147    166    177    186    190    195    204
##   [66,]    121    122    131    153    160    170    182    182    188
##   [67,]    121    121    131    139    142    149    149    151    164
##   [68,]    121    121    122    125    121    126    121    121    130
##   [69,]    121    121    121    121    121    121    122    121    121
##   [70,]    121    121    118    110    113    117    121    121    132
##   [71,]    108    121    102    101    106    113    121    121    135
##   [72,]     90     87     82     73     91    103    116    121    135
##   [73,]     69     71     64     60     69     85    100    112    129
##   [74,]     62     62     61     60     60     67     86    101    120
##   [75,]     60     60     59     59     60     60     73     85    105
##   [76,]     57     55     57     57     59     63     65     67     91
##   [77,]     53     52     53     52     54     56     60     60     73
##   [78,]     50     48     48     46     47     49     53     56     67
##   [79,]     46     43     42     40     40     41     45     48     57
##   [80,]     44     40     39     36     35     35     38     41     49
##   [81,]     40     36     33     29     27     26     28     29     35
##   [82,]     36     31     26     23     19     17     16     17     20
##   [83,]     32     26     20     16     11      8      4      4      5
##         [,371] [,372] [,373] [,374] [,375] [,376] [,377] [,378] [,379]
##    [1,]    194    194    196    193    192    198    216    231    239
##    [2,]    186    187    190    187    184    195    214    230    233
##    [3,]    182    182    185    181    178    185    202    215    219
##    [4,]    175    175    176    170    169    172    182    192    191
##    [5,]    167    164    163    159    157    161    167    173    178
##    [6,]    155    151    149    146    145    149    154    158    163
##    [7,]    144    139    137    135    134    138    142    144    148
##    [8,]    134    131    129    126    126    128    130    133    135
##    [9,]    130    131    130    126    124    125    125    125    126
##   [10,]    132    136    132    129    130    128    127    129    127
##   [11,]    138    144    134    147    137    132    148    136    133
##   [12,]    148    152    185    190    193    194    198    192    157
##   [13,]    182    184    202    212    225    230    243    243    196
##   [14,]    191    208    223    236    248    256    258    253    209
##   [15,]    205    225    243    256    270    285    280    268    249
##   [16,]    213    237    250    268    288    304    304    282    252
##   [17,]    218    239    256    272    295    302    303    304    268
##   [18,]    211    227    243    257    276    293    304    304    295
##   [19,]    198    215    233    243    261    291    304    304    304
##   [20,]    182    202    223    235    243    304    302    304    304
##   [21,]    164    190    213    228    243    284    304    304    304
##   [22,]    151    186    202    216    229    243    263    282    289
##   [23,]    129    160    188    200    212    224    236    252    268
##   [24,]    121    131    161    182    194    206    215    225    243
##   [25,]    121    121    131    152    172    188    191    193    215
##   [26,]    121    121    121    121    142    155    167    179    182
##   [27,]    136    121    121    121    121    138    151    176    182
##   [28,]    157    130    121    121    121    121    131    179    195
##   [29,]    182    150    121    121    121    121    121    166    189
##   [30,]    208    169    121    121    121    121    127    147    174
##   [31,]    243    195    148    121    121    121    121    129    151
##   [32,]    250    207    165    148    130    121    121    121    129
##   [33,]    263    213    182    167    153    137    121    121    121
##   [34,]    270    233    203    190    175    160    155    138    121
##   [35,]    256    233    227    220    201    182    182    179    182
##   [36,]    276    256    252    243    222    209    192    188    189
##   [37,]    297    286    277    258    249    235    220    219    208
##   [38,]    320    304    291    279    271    259    243    243    228
##   [39,]    365    331    313    298    296    292    278    267    248
##   [40,]    396    365    345    351    365    324    304    294    261
##   [41,]    421    396    383    383    376    369    352    313    281
##   [42,]    426    426    426    426    404    385    365    342    304
##   [43,]    426    428    432    434    430    416    395    374    350
##   [44,]    426    430    439    448    445    436    426    402    381
##   [45,]    426    434    449    466    465    455    441    425    415
##   [46,]    417    438    460    487    487    474    456    444    439
##   [47,]    402    426    458    487    487    487    464    454    452
##   [48,]    386    426    443    455    471    478    474    469    471
##   [49,]    376    406    426    438    450    457    466    477    482
##   [50,]    363    391    406    420    432    442    456    475    484
##   [51,]    347    375    392    404    415    426    453    487    487
##   [52,]    318    365    378    390    402    413    431    471    478
##   [53,]    301    331    365    376    389    401    420    438    451
##   [54,]    295    304    332    365    376    388    405    421    432
##   [55,]    290    299    304    331    365    374    390    406    417
##   [56,]    284    293    299    304    329    355    376    392    405
##   [57,]    278    287    294    300    304    332    358    377    395
##   [58,]    274    283    290    298    304    321    348    365    389
##   [59,]    267    276    284    293    302    309    339    365    380
##   [60,]    256    266    277    287    297    304    333    365    373
##   [61,]    242    250    268    283    297    304    325    342    354
##   [62,]    238    243    262    281    304    308    314    321    331
##   [63,]    237    243    258    270    281    293    296    300    311
##   [64,]    231    243    251    256    260    270    273    279    285
##   [65,]    215    223    231    235    240    250    251    252    263
##   [66,]    196    200    201    210    225    233    240    243    243
##   [67,]    177    181    182    189    211    224    235    242    243
##   [68,]    161    176    182    194    201    217    235    243    243
##   [69,]    154    175    182    196    209    219    239    242    243
##   [70,]    158    182    187    199    212    225    243    243    243
##   [71,]    158    170    182    199    210    220    236    243    243
##   [72,]    153    168    182    193    202    210    219    231    235
##   [73,]    149    164    182    188    192    196    198    201    210
##   [74,]    137    153    163    175    183    184    172    172    189
##   [75,]    121    139    147    154    155    152    141    121    121
##   [76,]    115    126    128    130    128    127    112    110    129
##   [77,]     99    104    108    107    106     98     85     91    103
##   [78,]     84     87     89     86     84     72     62     69     91
##   [79,]     70     69     71     71     67     62     60     60     78
##   [80,]     60     60     64     64     60     60     61     60     75
##   [81,]     42     49     54     53     55     57     60     60     64
##   [82,]     27     32     37     37     44     52     60     60     60
##   [83,]     13     16     23     25     32     40     50     55     55
##         [,380] [,381] [,382] [,383] [,384] [,385] [,386] [,387] [,388]
##    [1,]    242    246    249    262    274    284    294    302    306
##    [2,]    232    233    237    257    272    281    289    300    303
##    [3,]    220    215    220    240    251    263    278    291    295
##    [4,]    195    194    199    210    222    234    249    265    281
##    [5,]    178    179    183    193    206    218    231    249    267
##    [6,]    165    169    173    181    192    204    221    235    252
##    [7,]    153    160    167    174    183    195    211    228    241
##    [8,]    141    149    158    169    178    190    200    213    225
##    [9,]    130    137    142    154    168    181    189    199    209
##   [10,]    124    128    131    137    148    163    175    187    194
##   [11,]    126    123    123    126    133    151    166    178    183
##   [12,]    129    121    121    121    121    130    174    180    181
##   [13,]    155    139    121    121    121    182    182    182    182
##   [14,]    176    168    175    186    196    217    228    202    182
##   [15,]    182    182    191    206    220    244    259    255    259
##   [16,]    182    182    199    212    226    251    274    289    304
##   [17,]    213    182    203    218    230    257    297    301    302
##   [18,]    265    243    217    228    235    259    304    306    305
##   [19,]    294    274    261    259    258    278    304    310    315
##   [20,]    304    304    304    304    292    299    315    318    326
##   [21,]    304    304    304    304    304    309    323    330    340
##   [22,]    304    304    304    304    304    315    330    341    355
##   [23,]    283    294    300    304    304    317    332    345    360
##   [24,]    259    269    277    291    304    309    325    338    352
##   [25,]    235    256    261    275    288    302    317    332    347
##   [26,]    213    237    243    251    274    297    307    318    330
##   [27,]    203    226    243    257    265    294    304    306    304
##   [28,]    206    222    243    252    263    277    292    298    300
##   [29,]    202    215    227    243    252    259    262    274    287
##   [30,]    188    200    212    222    236    243    242    252    269
##   [31,]    166    182    194    199    213    226    237    243    252
##   [32,]    144    159    170    178    190    206    223    232    243
##   [33,]    121    136    139    153    169    189    207    215    228
##   [34,]    121    121    121    129    144    164    188    191    206
##   [35,]    142    121    121    121    121    132    155    170    182
##   [36,]    182    148    121    121    121    121    138    145    149
##   [37,]    196    186    167    133    121    121    121    121    121
##   [38,]    212    195    182    161    131    121    121    121    121
##   [39,]    234    208    190    176    158    153    152    152    145
##   [40,]    243    225    209    197    182    182    182    182    182
##   [41,]    255    238    226    219    215    216    218    228    208
##   [42,]    285    265    243    243    243    243    243    245    243
##   [43,]    319    294    279    272    276    289    292    272    257
##   [44,]    365    365    304    298    300    314    312    304    283
##   [45,]    413    391    374    335    329    340    337    323    309
##   [46,]    434    426    405    384    365    365    365    345    320
##   [47,]    450    441    426    406    384    367    365    365    324
##   [48,]    478    475    455    433    405    367    360    331    314
##   [49,]    487    487    487    449    419    384    365    304    296
##   [50,]    486    487    469    455    433    393    365    304    285
##   [51,]    486    487    468    454    433    396    365    304    290
##   [52,]    478    467    459    450    432    399    365    325    300
##   [53,]    456    452    448    441    431    411    391    365    304
##   [54,]    440    438    436    434    431    428    417    397    376
##   [55,]    426    429    429    430    431    431    430    426    406
##   [56,]    417    426    426    429    433    436    437    437    435
##   [57,]    410    422    426    431    436    442    447    452    459
##   [58,]    406    426    428    433    439    447    455    464    475
##   [59,]    393    403    417    429    431    443    455    470    487
##   [60,]    377    382    388    391    405    426    444    464    487
##   [61,]    357    357    357    359    369    397    418    439    487
##   [62,]    333    334    334    338    353    365    398    426    426
##   [63,]    311    312    312    315    338    359    373    393    405
##   [64,]    292    298    302    304    318    342    352    365    365
##   [65,]    276    290    301    309    320    326    333    336    334
##   [66,]    261    285    304    304    307    309    311    311    304
##   [67,]    253    277    304    304    304    304    304    304    286
##   [68,]    260    275    285    296    274    274    259    253    243
##   [69,]    256    267    277    272    258    243    248    244    243
##   [70,]    247    252    256    251    242    241    242    243    243
##   [71,]    243    243    243    239    234    237    238    240    242
##   [72,]    236    235    230    224    227    231    234    238    241
##   [73,]    216    214    213    212    219    225    229    234    239
##   [74,]    198    198    198    200    211    217    223    230    239
##   [75,]    182    182    182    187    201    208    215    223    243
##   [76,]    123    121    137    175    187    190    192    194    195
##   [77,]    117    121    136    154    182    164    166    169    174
##   [78,]    110    121    130    142    146    145    150    156    165
##   [79,]    102    121    121    124    125    120    128    138    148
##   [80,]     89    101    121     96     94    105    114    121    131
##   [81,]     70     72     69     67     68     83     96    109    118
##   [82,]     60     58     59     60     60     67     81     97    111
##   [83,]     52     53     55     58     60     60     66     89    108
##         [,389] [,390] [,391] [,392] [,393] [,394] [,395] [,396] [,397]
##    [1,]    322    342    357    368    374    371    362    357    357
##    [2,]    320    341    356    369    377    376    370    367    365
##    [3,]    311    332    351    368    379    385    380    373    368
##    [4,]    296    315    343    371    387    399    395    381    370
##    [5,]    286    305    338    375    402    416    411    390    370
##    [6,]    269    286    323    363    393    411    398    385    363
##    [7,]    255    271    294    329    357    370    364    350    337
##    [8,]    237    251    268    293    315    325    314    306    296
##    [9,]    216    229    241    256    269    274    273    267    256
##   [10,]    199    206    216    227    239    239    232    228    225
##   [11,]    186    190    196    202    203    194    200    197    199
##   [12,]    182    182    182    182    182    182    184    183    182
##   [13,]    182    182    182    182    182    182    182    182    187
##   [14,]    182    182    182    182    182    182    182    182    189
##   [15,]    250    213    192    182    182    182    182    182    192
##   [16,]    281    258    243    223    182    182    182    182    182
##   [17,]    304    280    268    255    247    213    182    182    182
##   [18,]    304    294    284    276    269    256    243    182    182
##   [19,]    313    308    299    295    295    280    265    252    213
##   [20,]    328    324    322    309    310    304    289    281    262
##   [21,]    346    344    343    340    336    324    314    308    294
##   [22,]    365    365    365    365    365    349    339    327    315
##   [23,]    364    365    369    375    377    372    359    347    334
##   [24,]    365    365    373    386    398    400    390    365    353
##   [25,]    365    365    377    394    414    426    426    394    365
##   [26,]    347    365    383    406    426    425    426    427    411
##   [27,]    324    348    374    398    411    426    426    430    434
##   [28,]    304    328    362    383    397    411    426    436    459
##   [29,]    298    304    338    365    379    396    412    426    487
##   [30,]    285    298    318    341    357    374    393    415    436
##   [31,]    270    282    298    319    334    350    365    385    405
##   [32,]    256    268    280    296    312    327    339    352    375
##   [33,]    243    253    259    267    278    304    309    304    304
##   [34,]    215    226    230    233    235    240    274    259    279
##   [35,]    182    182    191    202    211    223    231    240    243
##   [36,]    160    162    178    182    196    210    222    233    243
##   [37,]    130    131    150    169    182    194    207    220    232
##   [38,]    121    121    121    143    162    182    192    205    218
##   [39,]    130    121    121    121    132    152    172    188    200
##   [40,]    161    140    121    121    121    121    142    164    182
##   [41,]    191    172    142    121    121    121    121    140    160
##   [42,]    222    199    172    142    121    121    121    121    141
##   [43,]    243    224    198    172    152    130    121    121    126
##   [44,]    263    243    219    195    182    155    121    121    121
##   [45,]    294    263    236    209    192    182    151    130    121
##   [46,]    304    278    250    219    192    182    163    153    126
##   [47,]    304    282    252    223    182    175    170    166    150
##   [48,]    299    277    252    231    186    182    181    189    179
##   [49,]    278    260    245    222    212    203    209    209    201
##   [50,]    268    243    244    238    232    234    235    235    222
##   [51,]    276    263    243    243    243    260    263    252    243
##   [52,]    294    294    286    335    292    292    294    279    262
##   [53,]    304    335    365    355    365    335    324    304    279
##   [54,]    335    375    397    411    389    371    365    330    290
##   [55,]    406    405    426    426    426    393    365    345    293
##   [56,]    437    441    435    446    426    411    384    365    298
##   [57,]    470    480    477    487    470    426    400    365    331
##   [58,]    487    484    487    487    463    454    426    392    356
##   [59,]    485    486    487    487    472    451    426    409    390
##   [60,]    487    486    487    487    487    469    447    426    426
##   [61,]    469    468    481    487    487    480    465    458    455
##   [62,]    426    435    458    467    474    481    480    480    484
##   [63,]    398    408    434    448    460    472    486    487    486
##   [64,]    365    365    398    426    441    456    473    487    487
##   [65,]    341    349    362    381    416    434    456    470    483
##   [66,]    318    331    352    365    392    426    442    457    476
##   [67,]    304    315    345    365    385    426    435    457    487
##   [68,]    265    297    323    348    365    396    426    435    438
##   [69,]    243    281    304    337    365    381    390    398    405
##   [70,]    243    274    304    325    342    357    368    366    374
##   [71,]    243    272    304    314    327    337    342    343    349
##   [72,]    243    267    289    304    310    316    319    318    326
##   [73,]    243    261    278    289    304    304    304    304    304
##   [74,]    243    254    262    268    271    273    282    294    304
##   [75,]    243    243    243    243    243    243    260    282    304
##   [76,]    192    184    198    219    231    243    243    256    279
##   [77,]    178    182    192    192    212    225    235    241    243
##   [78,]    173    182    182    182    196    216    226    238    243
##   [79,]    160    173    180    182    189    205    220    237    247
##   [80,]    150    169    179    182    196    209    220    239    257
##   [81,]    139    168    182    191    200    211    224    243    254
##   [82,]    132    166    182    191    199    207    216    235    249
##   [83,]    134    176    181    185    189    193    197    203    213
##         [,398] [,399] [,400] [,401] [,402] [,403] [,404] [,405] [,406]
##    [1,]    355    356    360    368    376    379    387    397    406
##    [2,]    362    362    366    372    378    385    392    400    409
##    [3,]    362    360    364    369    377    383    392    402    412
##    [4,]    358    348    349    360    369    373    387    405    415
##    [5,]    352    335    321    339    354    355    373    392    408
##    [6,]    340    319    306    304    310    323    350    370    380
##    [7,]    316    297    288    282    290    299    317    341    353
##    [8,]    283    272    268    266    269    275    286    304    315
##    [9,]    256    251    252    252    254    256    268    279    288
##   [10,]    231    236    241    243    244    245    254    259    264
##   [11,]    211    225    236    240    242    242    245    248    250
##   [12,]    194    223    235    239    241    242    243    243    243
##   [13,]    203    223    235    239    242    242    243    243    243
##   [14,]    200    222    238    243    243    243    243    248    243
##   [15,]    212    239    242    261    274    279    289    291    270
##   [16,]    209    231    243    283    304    304    308    313    304
##   [17,]    199    228    243    304    301    313    324    334    324
##   [18,]    205    225    235    243    304    321    339    359    349
##   [19,]    216    227    234    241    274    324    358    363    364
##   [20,]    238    233    235    239    243    304    365    365    365
##   [21,]    263    241    240    241    243    273    297    350    365
##   [22,]    294    270    243    243    264    272    290    314    365
##   [23,]    317    308    292    281    282    288    294    302    351
##   [24,]    337    326    316    304    304    304    304    316    339
##   [25,]    348    338    331    328    325    324    324    333    349
##   [26,]    370    358    356    356    355    355    355    357    360
##   [27,]    415    396    396    396    396    396    396    396    402
##   [28,]    462    457    441    438    438    441    441    441    441
##   [29,]    485    487    487    472    474    487    487    487    487
##   [30,]    469    473    474    475    483    486    486    487    480
##   [31,]    426    441    449    455    471    487    487    471    459
##   [32,]    382    408    416    423    441    474    481    456    434
##   [33,]    344    365    388    406    426    441    452    441    426
##   [34,]    307    340    357    376    396    426    434    437    426
##   [35,]    290    316    334    353    365    405    427    428    410
##   [36,]    271    304    321    343    365    386    415    398    385
##   [37,]    253    279    295    317    349    371    374    375    348
##   [38,]    236    258    266    284    304    304    304    304    304
##   [39,]    214    231    238    254    268    273    278    278    269
##   [40,]    190    201    214    232    243    243    252    252    243
##   [41,]    177    182    190    213    220    228    233    228    214
##   [42,]    165    179    182    200    203    207    206    196    182
##   [43,]    157    182    186    189    190    189    188    183    183
##   [44,]    137    158    182    182    182    182    181    180    181
##   [45,]    121    140    154    165    172    175    177    179    181
##   [46,]    121    121    129    141    157    166    173    179    181
##   [47,]    121    121    121    121    148    159    170    180    182
##   [48,]    170    148    137    145    150    159    171    180    182
##   [49,]    189    182    168    168    165    167    171    178    182
##   [50,]    210    197    187    182    179    176    176    179    182
##   [51,]    228    213    196    182    182    182    181    181    181
##   [52,]    246    234    207    190    182    182    182    182    182
##   [53,]    252    243    221    207    202    191    182    182    182
##   [54,]    247    241    230    222    222    218    196    189    184
##   [55,]    265    243    241    240    243    243    226    209    193
##   [56,]    276    261    243    243    261    259    243    224    203
##   [57,]    297    282    282    283    292    293    260    243    224
##   [58,]    333    304    304    304    302    296    275    259    243
##   [59,]    381    372    350    330    316    299    281    273    264
##   [60,]    426    403    383    365    344    314    294    289    287
##   [61,]    444    432    416    395    374    345    318    303    319
##   [62,]    471    450    435    426    400    373    365    365    365
##   [63,]    487    465    447    432    420    402    390    385    377
##   [64,]    487    471    459    448    437    426    413    404    395
##   [65,]    480    476    472    462    453    446    432    421    411
##   [66,]    487    487    487    477    470    468    455    443    426
##   [67,]    487    487    487    487    481    484    471    464    445
##   [68,]    441    462    468    476    480    487    487    487    477
##   [69,]    414    426    426    447    461    487    487    487    449
##   [70,]    378    379    400    413    420    449    472    465    443
##   [71,]    352    359    365    382    389    418    440    446    438
##   [72,]    333    341    350    357    361    386    416    431    434
##   [73,]    315    325    332    336    341    358    385    411    426
##   [74,]    304    309    315    317    318    332    365    399    426
##   [75,]    304    304    304    304    304    321    365    395    426
##   [76,]    259    272    291    302    304    340    369    390    414
##   [77,]    247    243    283    304    332    363    374    379    386
##   [78,]    243    270    284    304    330    355    365    365    365
##   [79,]    264    280    304    302    323    335    344    348    355
##   [80,]    267    282    304    304    313    318    326    332    340
##   [81,]    259    271    283    294    294    301    310    318    326
##   [82,]    242    255    267    271    273    279    289    304    313
##   [83,]    204    230    249    250    251    252    255    261    286
##         [,407] [,408] [,409] [,410] [,411] [,412] [,413] [,414] [,415]
##    [1,]    418    419    431    434    432    426    420    414    407
##    [2,]    419    425    433    439    437    432    428    422    416
##    [3,]    421    426    433    436    434    431    427    422    417
##    [4,]    421    424    425    426    426    423    420    417    414
##    [5,]    413    413    413    416    415    410    410    411    411
##    [6,]    389    391    393    393    396    396    401    404    408
##    [7,]    358    362    367    369    374    379    388    392    398
##    [8,]    326    332    338    341    353    361    371    375    382
##    [9,]    297    303    307    312    323    338    351    354    363
##   [10,]    273    277    279    282    293    306    319    331    344
##   [11,]    255    257    257    258    264    282    294    308    326
##   [12,]    243    243    243    243    243    265    296    304    304
##   [13,]    243    243    243    243    258    282    304    311    323
##   [14,]    243    243    243    250    269    297    307    319    331
##   [15,]    253    243    243    249    276    300    316    331    347
##   [16,]    283    263    243    264    271    297    320    339    365
##   [17,]    311    294    283    281    289    297    309    331    349
##   [18,]    334    319    304    298    297    300    304    321    344
##   [19,]    357    342    327    312    303    302    304    310    338
##   [20,]    365    365    350    334    313    304    304    304    324
##   [21,]    365    367    367    357    344    318    309    304    316
##   [22,]    365    372    377    381    369    349    334    333    334
##   [23,]    365    380    386    394    381    365    350    349    350
##   [24,]    365    390    405    418    401    383    372    362    363
##   [25,]    365    396    426    425    420    402    393    386    374
##   [26,]    377    400    426    444    438    420    418    406    400
##   [27,]    402    413    426    467    465    460    446    426    426
##   [28,]    441    446    475    484    487    487    487    487    472
##   [29,]    487    487    487    487    487    487    487    487    487
##   [30,]    477    474    467    465    467    480    487    487    487
##   [31,]    448    443    442    442    443    450    462    487    487
##   [32,]    424    418    415    411    413    416    421    442    468
##   [33,]    409    393    380    365    374    385    398    411    426
##   [34,]    398    380    365    338    355    365    381    389    392
##   [35,]    375    348    317    300    291    298    335    335    335
##   [36,]    365    304    295    275    252    266    270    274    291
##   [37,]    318    299    276    258    224    226    232    239    255
##   [38,]    291    271    257    235    192    182    200    215    224
##   [39,]    265    261    255    248    198    186    183    190    202
##   [40,]    243    243    243    243    227    182    182    183    182
##   [41,]    198    198    198    198    201    187    183    182    182
##   [42,]    187    183    182    182    182    184    183    182    182
##   [43,]    182    182    182    182    182    182    183    182    182
##   [44,]    181    182    182    182    182    182    182    200    208
##   [45,]    181    182    182    182    182    213    219    219    226
##   [46,]    182    186    191    211    233    242    246    248    252
##   [47,]    191    198    213    236    242    247    252    261    278
##   [48,]    196    209    221    239    248    252    259    274    297
##   [49,]    194    206    216    229    243    243    243    262    274
##   [50,]    190    199    206    219    230    236    242    243    243
##   [51,]    182    189    194    207    222    232    243    243    243
##   [52,]    182    182    182    193    210    223    234    243    243
##   [53,]    182    182    182    182    196    213    229    243    243
##   [54,]    182    182    182    182    182    199    221    243    243
##   [55,]    182    182    182    182    182    182    206    224    243
##   [56,]    182    182    182    182    182    182    194    211    227
##   [57,]    207    193    186    182    182    182    182    190    205
##   [58,]    228    218    206    188    182    182    182    182    182
##   [59,]    252    237    225    206    189    182    182    182    182
##   [60,]    281    262    243    225    210    203    190    182    182
##   [61,]    311    294    273    245    235    223    212    202    189
##   [62,]    342    322    304    277    253    243    231    226    212
##   [63,]    370    355    334    305    281    270    261    253    235
##   [64,]    385    375    365    335    304    304    304    304    279
##   [65,]    401    390    380    363    340    336    324    316    304
##   [66,]    416    406    395    381    365    365    355    352    347
##   [67,]    426    416    406    391    384    381    381    377    369
##   [68,]    442    430    421    407    404    404    403    393    380
##   [69,]    444    434    428    423    426    426    426    411    388
##   [70,]    435    432    429    427    426    426    426    414    389
##   [71,]    434    431    429    427    427    426    414    398    378
##   [72,]    433    432    429    427    427    426    406    387    365
##   [73,]    428    429    429    427    427    426    407    386    365
##   [74,]    426    426    427    427    427    426    411    390    365
##   [75,]    426    426    426    426    426    426    426    402    385
##   [76,]    426    426    426    426    426    426    426    414    397
##   [77,]    404    426    426    426    426    426    426    426    419
##   [78,]    386    398    421    426    426    426    426    426    426
##   [79,]    361    373    396    419    426    426    426    426    426
##   [80,]    347    356    373    396    411    426    426    426    426
##   [81,]    331    341    356    373    388    406    418    423    426
##   [82,]    315    326    343    359    365    390    400    408    412
##   [83,]    298    310    331    352    365    377    386    393    398
##         [,416] [,417] [,418] [,419] [,420] [,421] [,422] [,423] [,424]
##    [1,]    403    397    388    378    368    355    345    333    325
##    [2,]    410    404    392    380    371    362    352    342    330
##    [3,]    412    406    392    380    371    362    354    344    331
##    [4,]    411    405    390    377    369    362    355    342    326
##    [5,]    410    407    393    378    371    365    358    347    334
##    [6,]    412    415    410    396    380    372    364    354    343
##    [7,]    412    414    418    416    398    382    371    362    352
##    [8,]    393    405    410    401    390    380    373    368    361
##    [9,]    375    385    396    392    382    377    374    371    367
##   [10,]    357    368    380    380    376    376    376    373    370
##   [11,]    341    353    367    371    372    376    380    377    378
##   [12,]    338    351    360    365    367    381    391    399    391
##   [13,]    336    348    359    365    377    397    419    424    417
##   [14,]    341    354    362    383    396    414    426    426    424
##   [15,]    359    367    382    404    419    424    424    425    426
##   [16,]    363    379    405    426    423    425    424    425    426
##   [17,]    365    392    421    424    425    425    425    425    426
##   [18,]    365    395    426    426    426    425    426    426    426
##   [19,]    365    389    421    426    426    426    426    426    427
##   [20,]    365    377    415    426    426    426    427    427    428
##   [21,]    341    365    411    426    426    426    427    428    429
##   [22,]    349    365    409    426    426    427    428    430    432
##   [23,]    353    365    406    426    426    428    430    433    435
##   [24,]    362    362    382    426    426    432    439    445    450
##   [25,]    365    364    380    411    426    445    461    473    487
##   [26,]    391    385    397    412    426    454    480    485    479
##   [27,]    426    426    421    420    426    458    469    487    458
##   [28,]    458    453    445    444    451    461    457    446    435
##   [29,]    487    480    483    487    487    487    458    426    427
##   [30,]    487    487    496    517    499    487    481    451    424
##   [31,]    487    487    492    494    491    493    487    452    422
##   [32,]    472    484    487    489    488    480    466    453    433
##   [33,]    426    451    465    466    465    462    455    448    432
##   [34,]    413    426    444    446    451    449    447    441    430
##   [35,]    376    382    408    420    432    435    435    433    423
##   [36,]    304    325    365    387    408    426    428    426    405
##   [37,]    257    287    321    350    375    382    405    394    386
##   [38,]    235    254    285    304    327    352    365    365    365
##   [39,]    214    232    254    274    294    315    330    334    330
##   [40,]    195    213    231    243    263    284    304    304    304
##   [41,]    182    195    213    229    240    253    256    271    271
##   [42,]    182    182    194    218    231    238    242    243    243
##   [43,]    190    196    199    212    227    237    241    243    254
##   [44,]    214    236    243    232    232    243    243    265    275
##   [45,]    231    248    252    243    243    260    280    280    298
##   [46,]    257    277    280    281    292    290    300    304    322
##   [47,]    290    304    304    304    309    304    304    317    334
##   [48,]    303    315    334    340    341    350    350    353    352
##   [49,]    304    331    365    365    365    362    365    366    365
##   [50,]    258    313    355    365    365    365    365    368    370
##   [51,]    270    287    304    304    345    365    365    371    378
##   [52,]    267    283    291    297    302    321    350    372    385
##   [53,]    262    275    283    288    293    299    304    350    376
##   [54,]    256    267    277    282    288    293    298    320    365
##   [55,]    249    258    269    274    279    284    289    298    320
##   [56,]    243    252    260    265    271    275    279    287    297
##   [57,]    223    245    252    257    263    266    268    275    286
##   [58,]    205    228    243    249    254    256    258    263    275
##   [59,]    186    205    220    234    246    247    247    251    264
##   [60,]    182    182    197    205    217    222    223    237    252
##   [61,]    182    182    182    182    191    192    192    198    229
##   [62,]    191    182    182    182    182    182    182    182    182
##   [63,]    222    196    182    182    182    182    182    182    182
##   [64,]    250    243    219    213    195    182    182    182    182
##   [65,]    280    263    243    243    220    200    182    182    182
##   [66,]    321    311    291    284    257    233    208    182    182
##   [67,]    365    342    320    307    304    273    243    188    182
##   [68,]    368    355    332    312    305    274    231    183    183
##   [69,]    368    339    318    304    275    243    211    182    182
##   [70,]    355    326    304    285    267    243    198    182    182
##   [71,]    352    317    304    280    260    243    186    183    183
##   [72,]    338    304    285    266    249    233    190    183    183
##   [73,]    336    304    274    243    246    225    207    182    182
##   [74,]    340    304    280    254    243    238    223    211    198
##   [75,]    353    304    292    276    279    260    243    230    218
##   [76,]    374    337    304    289    303    295    275    243    231
##   [77,]    396    378    371    335    349    347    331    296    278
##   [78,]    419    408    402    399    396    386    371    365    365
##   [79,]    426    426    427    427    427    417    413    411    411
##   [80,]    426    426    428    430    431    434    439    446    446
##   [81,]    426    426    429    434    437    446    460    477    477
##   [82,]    423    426    432    439    445    454    477    484    487
##   [83,]    402    409    420    431    433    446    470    487    487
##         [,425] [,426] [,427] [,428] [,429] [,430] [,431] [,432] [,433]
##    [1,]    313    302    295    288    281    273    259    249    237
##    [2,]    317    304    298    295    290    279    266    253    242
##    [3,]    317    304    299    298    295    281    266    253    244
##    [4,]    314    309    305    306    304    296    279    260    251
##    [5,]    323    317    316    316    313    308    297    280    262
##    [6,]    334    329    327    327    323    316    308    298    285
##    [7,]    345    342    340    338    332    323    314    306    299
##    [8,]    356    353    351    348    339    328    317    309    305
##    [9,]    364    362    360    357    346    332    319    310    306
##   [10,]    367    365    365    362    349    331    318    310    306
##   [11,]    369    366    365    360    348    331    317    308    304
##   [12,]    370    365    365    365    346    327    306    304    299
##   [13,]    395    372    365    365    350    330    311    304    290
##   [14,]    418    389    375    365    356    336    311    292    283
##   [15,]    423    402    386    373    365    337    307    295    284
##   [16,]    420    400    390    376    365    338    314    304    295
##   [17,]    415    398    385    369    360    345    334    322    314
##   [18,]    419    399    385    365    358    353    351    347    338
##   [19,]    424    410    397    388    373    364    367    365    359
##   [20,]    427    426    414    409    395    384    371    367    365
##   [21,]    429    427    426    426    418    395    376    367    365
##   [22,]    431    429    427    426    405    395    371    365    337
##   [23,]    434    429    426    412    397    378    361    338    324
##   [24,]    446    427    418    401    381    365    348    326    304
##   [25,]    487    426    408    390    365    367    347    325    304
##   [26,]    453    426    414    398    385    371    356    334    321
##   [27,]    440    436    426    410    397    384    369    348    332
##   [28,]    432    430    427    423    411    397    376    361    343
##   [29,]    423    426    426    427    426    410    388    365    356
##   [30,]    413    403    403    418    426    422    400    379    369
##   [31,]    398    380    365    387    409    426    413    388    379
##   [32,]    395    365    368    366    379    426    406    393    384
##   [33,]    400    382    365    365    365    382    390    394    395
##   [34,]    405    383    365    365    365    365    382    400    408
##   [35,]    401    383    365    365    364    365    386    403    414
##   [36,]    390    379    365    364    364    365    391    409    417
##   [37,]    378    369    363    362    363    365    416    426    424
##   [38,]    365    342    349    354    359    365    426    426    426
##   [39,]    316    314    317    335    351    375    410    411    394
##   [40,]    300    301    303    304    331    359    381    380    377
##   [41,]    284    295    301    304    310    354    366    370    370
##   [42,]    273    290    300    304    327    352    367    369    368
##   [43,]    274    294    304    319    331    356    370    370    369
##   [44,]    298    312    327    338    346    360    374    374    371
##   [45,]    318    334    350    365    365    377    391    382    373
##   [46,]    338    357    366    380    394    421    426    406    386
##   [47,]    349    365    374    391    413    426    426    426    406
##   [48,]    355    359    365    398    426    425    426    426    421
##   [49,]    361    362    365    399    426    426    426    426    426
##   [50,]    368    365    399    416    422    425    426    426    414
##   [51,]    381    401    426    422    425    425    405    389    393
##   [52,]    394    406    426    426    425    402    375    357    350
##   [53,]    388    400    410    426    426    380    345    324    304
##   [54,]    377    389    398    411    426    379    324    304    311
##   [55,]    350    371    374    389    385    374    304    306    305
##   [56,]    304    327    352    365    371    368    336    304    304
##   [57,]    293    301    315    336    357    366    345    315    304
##   [58,]    282    290    298    304    331    365    365    334    304
##   [59,]    272    280    288    296    311    357    365    358    333
##   [60,]    260    269    278    288    300    331    365    365    353
##   [61,]    248    257    267    277    292    304    333    357    365
##   [62,]    218    243    254    265    284    304    316    341    356
##   [63,]    190    217    236    249    272    298    304    334    353
##   [64,]    182    199    219    234    261    304    319    332    354
##   [65,]    182    191    211    229    258    304    325    343    365
##   [66,]    182    182    205    225    259    304    327    348    365
##   [67,]    182    182    205    224    259    304    334    356    359
##   [68,]    182    198    212    229    262    304    355    365    364
##   [69,]    182    201    220    243    284    318    365    365    331
##   [70,]    182    195    213    234    260    290    298    316    314
##   [71,]    182    182    196    212    234    259    266    270    267
##   [72,]    182    182    182    190    197    213    228    228    233
##   [73,]    182    182    182    182    182    182    182    182    200
##   [74,]    192    186    182    182    182    182    182    182    182
##   [75,]    215    205    200    198    197    192    182    182    224
##   [76,]    229    218    215    213    212    210    210    219    227
##   [77,]    264    237    236    236    234    237    238    243    238
##   [78,]    365    304    304    263    258    274    267    256    247
##   [79,]    406    383    372    335    335    314    293    276    257
##   [80,]    435    426    405    391    376    365    331    304    272
##   [81,]    462    447    433    418    397    376    365    322    297
##   [82,]    487    472    456    441    417    389    365    350    330
##   [83,]    487    487    479    464    441    416    396    375    356
##         [,434] [,435] [,436] [,437] [,438] [,439] [,440] [,441] [,442]
##    [1,]    224    215    211    216    218    230    235    250    249
##    [2,]    234    227    222    223    227    234    239    252    251
##    [3,]    237    230    227    227    231    236    241    253    253
##    [4,]    243    239    236    236    238    240    243    247    260
##    [5,]    254    253    250    250    252    253    254    258    271
##    [6,]    273    270    270    271    269    272    271    275    289
##    [7,]    291    292    289    291    292    292    295    297    309
##    [8,]    302    302    302    303    305    307    309    319    331
##    [9,]    304    304    304    305    310    316    323    338    351
##   [10,]    304    303    302    304    309    317    331    348    352
##   [11,]    302    299    295    296    297    306    319    336    349
##   [12,]    294    289    284    284    284    293    304    304    325
##   [13,]    279    265    254    253    253    261    257    278    295
##   [14,]    267    243    247    244    243    243    245    243    264
##   [15,]    275    264    251    244    243    243    243    243    243
##   [16,]    291    280    271    268    258    243    243    243    243
##   [17,]    309    298    296    295    287    265    251    243    243
##   [18,]    331    324    320    314    306    289    274    259    246
##   [19,]    356    345    343    327    313    305    297    269    254
##   [20,]    365    365    365    337    317    307    304    275    255
##   [21,]    351    345    332    331    315    307    304    276    254
##   [22,]    324    314    300    295    294    289    272    253    243
##   [23,]    304    293    277    266    264    259    252    250    245
##   [24,]    293    276    252    244    242    246    245    244    245
##   [25,]    294    278    263    244    237    227    213    213    213
##   [26,]    309    297    276    255    237    216    193    182    182
##   [27,]    317    304    292    267    243    231    215    205    197
##   [28,]    327    311    300    279    260    249    236    224    219
##   [29,]    341    324    304    291    274    264    253    243    238
##   [30,]    359    343    326    305    289    279    268    257    248
##   [31,]    372    365    344    323    304    294    282    268    257
##   [32,]    377    365    355    335    316    304    291    275    261
##   [33,]    395    391    374    352    332    318    304    290    276
##   [34,]    417    426    405    375    350    335    320    304    292
##   [35,]    426    425    426    406    375    358    342    327    312
##   [36,]    426    426    426    426    406    385    365    350    335
##   [37,]    416    419    426    426    426    416    380    368    358
##   [38,]    402    392    401    426    426    381    380    371    368
##   [39,]    375    366    363    379    377    370    369    367    366
##   [40,]    365    358    351    314    335    345    365    348    353
##   [41,]    366    359    341    312    304    304    304    316    317
##   [42,]    367    366    365    339    310    304    304    304    304
##   [43,]    367    366    366    357    321    309    305    304    304
##   [44,]    367    365    365    358    322    312    307    305    304
##   [45,]    365    366    361    342    314    304    304    304    296
##   [46,]    372    365    355    325    306    306    302    296    287
##   [47,]    388    375    365    336    304    305    299    290    277
##   [48,]    401    385    369    341    326    311    300    288    272
##   [49,]    407    390    371    355    342    328    315    304    287
##   [50,]    399    386    373    366    359    343    326    313    304
##   [51,]    382    378    373    368    365    356    335    318    304
##   [52,]    354    361    368    367    366    353    336    319    304
##   [53,]    322    337    358    365    329    327    321    315    310
##   [54,]    304    320    333    324    304    304    314    311    308
##   [55,]    305    304    308    300    296    295    296    298    296
##   [56,]    304    303    298    288    281    278    274    278    276
##   [57,]    304    302    291    277    267    259    251    260    261
##   [58,]    304    299    284    267    253    243    246    243    248
##   [59,]    313    301    284    263    249    244    243    244    243
##   [60,]    335    317    294    270    259    252    243    243    243
##   [61,]    357    332    298    278    268    259    252    246    243
##   [62,]    365    365    301    286    276    267    259    252    245
##   [63,]    361    356    318    294    284    272    263    255    246
##   [64,]    365    352    315    296    287    277    267    258    248
##   [65,]    361    365    317    296    287    278    269    259    249
##   [66,]    365    365    319    295    286    275    265    254    245
##   [67,]    365    337    316    297    287    273    259    243    244
##   [68,]    331    314    311    306    298    278    261    247    243
##   [69,]    304    306    305    305    304    285    267    252    243
##   [70,]    291    284    292    299    304    274    260    247    243
##   [71,]    261    259    267    273    260    243    243    245    243
##   [72,]    239    243    249    247    244    245    243    243    243
##   [73,]    227    239    242    242    243    243    243    243    243
##   [74,]    223    237    241    242    242    242    242    243    243
##   [75,]    226    237    240    242    242    242    242    243    243
##   [76,]    234    237    240    242    242    242    242    243    243
##   [77,]    236    238    240    242    243    243    243    243    243
##   [78,]    243    241    241    242    243    243    243    243    243
##   [79,]    243    243    242    242    243    243    247    246    243
##   [80,]    243    243    243    243    243    243    253    259    249
##   [81,]    276    249    243    243    243    243    265    279    289
##   [82,]    304    274    243    243    243    243    284    304    311
##   [83,]    336    304    274    253    243    260    304    320    339
##         [,443] [,444] [,445] [,446] [,447] [,448] [,449] [,450] [,451]
##    [1,]    267    285    295    311    324    317    314    305    284
##    [2,]    268    285    297    314    326    318    315    306    284
##    [3,]    272    287    305    318    326    316    314    300    273
##    [4,]    274    292    305    317    319    314    309    297    280
##    [5,]    287    305    319    331    327    316    312    299    283
##    [6,]    301    319    337    345    343    334    323    309    295
##    [7,]    322    340    350    357    355    349    339    325    313
##    [8,]    344    352    359    362    362    360    353    341    327
##    [9,]    354    359    361    362    363    364    363    353    336
##   [10,]    356    358    352    356    360    363    365    357    339
##   [11,]    345    346    335    338    351    362    365    361    341
##   [12,]    330    333    313    304    324    365    365    365    351
##   [13,]    309    308    307    302    304    332    355    365    339
##   [14,]    277    285    292    296    304    316    331    365    322
##   [15,]    251    263    267    271    278    287    289    289    279
##   [16,]    243    243    243    243    243    243    243    243    213
##   [17,]    243    240    229    217    208    198    198    192    189
##   [18,]    243    236    214    196    182    186    182    180    181
##   [19,]    246    240    214    182    184    183    181    178    176
##   [20,]    245    244    243    182    182    182    178    175    169
##   [21,]    243    243    213    207    182    182    177    173    162
##   [22,]    245    243    213    196    190    184    179    177    155
##   [23,]    243    243    214    194    185    184    183    182    167
##   [24,]    243    229    209    188    180    176    175    172    153
##   [25,]    206    192    182    178    169    156    153    148    142
##   [26,]    182    183    174    165    156    130    129    126    128
##   [27,]    190    182    174    169    162    151    121    121    121
##   [28,]    213    206    199    198    193    186    183    167    167
##   [29,]    235    234    243    243    225    196    185    182    182
##   [30,]    244    243    242    243    213    189    184    181    176
##   [31,]    246    243    216    182    198    182    182    178    168
##   [32,]    243    243    222    204    182    182    182    182    182
##   [33,]    267    252    237    222    217    214    213    213    213
##   [34,]    283    268    253    243    243    243    243    243    243
##   [35,]    299    284    268    262    256    251    247    243    243
##   [36,]    320    299    284    275    267    258    250    243    243
##   [37,]    340    314    299    289    279    268    258    245    243
##   [38,]    357    334    317    304    293    281    270    250    243
##   [39,]    366    357    332    318    308    298    286    264    248
##   [40,]    365    365    341    326    316    309    304    277    259
##   [41,]    329    346    340    329    319    311    304    285    264
##   [42,]    304    304    314    319    316    311    304    289    272
##   [43,]    302    302    304    308    311    309    304    294    281
##   [44,]    295    294    297    302    305    305    305    302    292
##   [45,]    282    285    288    293    299    304    304    305    304
##   [46,]    270    275    277    283    291    300    304    305    313
##   [47,]    254    257    259    268    277    287    297    307    322
##   [48,]    247    243    243    250    262    274    286    304    332
##   [49,]    254    243    243    243    243    257    271    295    324
##   [50,]    269    243    243    243    243    243    258    281    296
##   [51,]    275    243    243    243    243    243    243    258    274
##   [52,]    277    243    243    243    243    243    243    243    258
##   [53,]    286    243    243    243    243    243    243    243    243
##   [54,]    287    256    243    243    243    243    243    243    243
##   [55,]    272    256    250    245    243    243    243    243    243
##   [56,]    268    256    249    243    244    243    243    243    243
##   [57,]    258    253    248    243    243    243    243    243    243
##   [58,]    249    248    246    243    243    243    243    243    243
##   [59,]    243    243    243    243    243    243    243    243    243
##   [60,]    243    243    243    243    243    243    243    243    243
##   [61,]    243    243    243    243    243    243    243    243    243
##   [62,]    243    243    243    243    243    243    243    243    243
##   [63,]    243    243    243    243    243    243    243    243    243
##   [64,]    243    243    243    243    243    243    243    243    243
##   [65,]    243    243    243    243    243    243    243    243    243
##   [66,]    244    244    243    243    243    243    243    243    243
##   [67,]    244    243    244    243    243    243    243    243    243
##   [68,]    243    243    243    243    243    243    243    243    243
##   [69,]    243    243    243    243    243    243    243    243    243
##   [70,]    243    243    243    243    243    243    243    243    243
##   [71,]    243    243    243    243    243    243    243    243    243
##   [72,]    243    243    243    243    243    243    244    252    260
##   [73,]    243    243    243    243    243    243    246    262    274
##   [74,]    243    243    243    243    243    243    252    263    279
##   [75,]    243    243    246    243    243    243    243    250    264
##   [76,]    243    253    258    256    243    243    243    243    243
##   [77,]    243    264    281    291    291    261    243    243    243
##   [78,]    243    277    304    308    309    294    263    243    243
##   [79,]    260    294    310    323    327    317    294    274    264
##   [80,]    284    304    325    340    349    344    323    304    304
##   [81,]    311    324    341    359    367    370    355    340    324
##   [82,]    331    344    365    370    380    388    380    365    350
##   [83,]    347    353    365    381    396    412    414    394    379
##         [,452] [,453] [,454] [,455] [,456] [,457] [,458] [,459] [,460]
##    [1,]    265    253    243    233    222    211    216    217    220
##    [2,]    265    253    242    234    227    223    223    227    229
##    [3,]    261    250    242    235    229    226    227    231    233
##    [4,]    261    250    243    237    232    230    232    236    239
##    [5,]    264    252    246    241    236    234    235    239    241
##    [6,]    283    269    255    250    242    239    238    240    242
##    [7,]    304    295    279    262    250    244    242    241    242
##    [8,]    313    307    297    283    266    254    246    243    242
##    [9,]    322    311    300    290    275    259    249    245    243
##   [10,]    321    312    303    291    277    261    251    246    243
##   [11,]    325    313    306    298    285    267    256    246    243
##   [12,]    315    308    306    305    304    289    273    243    243
##   [13,]    309    306    305    304    304    304    299    279    272
##   [14,]    304    304    304    304    304    304    304    304    290
##   [15,]    260    259    259    279    292    299    304    304    304
##   [16,]    213    225    235    243    260    273    284    304    284
##   [17,]    182    199    213    224    236    247    242    253    263
##   [18,]    181    182    194    202    210    232    225    234    243
##   [19,]    172    178    182    185    187    185    194    212    233
##   [20,]    154    161    170    182    182    178    182    191    216
##   [21,]    139    148    155    158    160    170    177    182    202
##   [22,]    128    128    130    131    139    151    165    176    187
##   [23,]    135    121    121    121    121    128    146    158    166
##   [24,]    135    128    123    121    119    119    128    140    134
##   [25,]    133    127    123    121    117    113    113    121     93
##   [26,]    124    122    121    117    114    103     90     69     63
##   [27,]    121    121    121    121    121    103     80     60     60
##   [28,]    172    180    182    167    137    119     90     78     66
##   [29,]    182    182    182    161    153    127    101     90     81
##   [30,]    171    154    148    153    141    127    106     99     92
##   [31,]    159    121    121    128    127    121    116    112    110
##   [32,]    182    161    135    121    121    121    121    121    121
##   [33,]    206    188    172    163    155    162    183    187    186
##   [34,]    243    205    191    182    182    188    195    201    204
##   [35,]    218    209    199    194    194    198    209    217    226
##   [36,]    222    212    205    201    202    206    219    227    235
##   [37,]    227    219    212    208    210    213    226    233    239
##   [38,]    234    227    219    216    217    220    231    237    241
##   [39,]    241    235    226    223    225    227    236    240    242
##   [40,]    249    243    234    231    231    235    239    242    243
##   [41,]    253    243    238    236    236    238    241    242    243
##   [42,]    261    249    243    242    243    241    243    243    243
##   [43,]    273    266    263    261    252    243    244    243    243
##   [44,]    288    284    283    278    266    256    250    244    243
##   [45,]    304    304    304    292    278    264    255    243    243
##   [46,]    320    325    321    310    294    279    268    258    249
##   [47,]    337    348    346    333    309    294    283    270    259
##   [48,]    358    365    365    357    318    306    299    283    267
##   [49,]    365    365    365    331    319    309    306    304    285
##   [50,]    318    343    339    329    317    309    306    305    293
##   [51,]    289    304    315    316    313    307    304    288    276
##   [52,]    274    289    304    304    304    304    284    276    265
##   [53,]    251    266    270    269    263    255    256    251    249
##   [54,]    243    243    243    243    245    243    243    243    243
##   [55,]    243    243    243    243    243    243    243    243    243
##   [56,]    243    243    243    243    243    243    243    243    243
##   [57,]    243    243    243    243    243    243    243    243    243
##   [58,]    243    243    243    243    243    243    243    243    243
##   [59,]    243    243    243    243    243    265    277    289    294
##   [60,]    243    243    247    246    257    284    304    300    308
##   [61,]    243    243    253    257    279    299    302    304    313
##   [62,]    243    254    261    269    288    299    301    304    320
##   [63,]    247    258    268    284    296    301    304    316    325
##   [64,]    250    264    279    300    304    304    304    318    332
##   [65,]    243    263    276    296    304    304    304    317    328
##   [66,]    246    254    261    279    299    304    304    312    318
##   [67,]    243    243    243    261    288    298    304    304    304
##   [68,]    243    243    243    246    282    294    299    302    303
##   [69,]    243    243    243    258    282    293    297    300    302
##   [70,]    243    250    256    268    285    293    298    300    302
##   [71,]    256    265    271    281    292    298    304    304    304
##   [72,]    271    282    288    296    305    309    314    314    321
##   [73,]    291    304    304    305    312    320    327    331    339
##   [74,]    304    301    304    307    317    327    336    346    356
##   [75,]    279    297    304    309    325    335    347    360    364
##   [76,]    258    281    297    310    328    339    350    357    365
##   [77,]    243    274    300    311    327    338    348    357    362
##   [78,]    243    275    304    316    330    341    351    359    365
##   [79,]    275    284    299    316    338    351    361    369    379
##   [80,]    295    293    298    316    346    365    371    381    392
##   [81,]    312    302    302    326    351    365    382    393    402
##   [82,]    342    339    337    355    365    407    394    402    408
##   [83,]    374    369    356    369    398    426    417    412    413
##         [,461] [,462] [,463] [,464] [,465] [,466] [,467] [,468] [,469]
##    [1,]    216    202    187    180    155    136    126    134    130
##    [2,]    226    207    193    187    159    141    130    134    139
##    [3,]    231    225    204    194    183    155    136    139    141
##    [4,]    240    236    224    206    190    176    161    148    142
##    [5,]    242    242    237    228    212    198    188    178    165
##    [6,]    242    243    243    241    230    221    206    192    179
##    [7,]    242    243    243    243    241    234    217    201    190
##    [8,]    243    243    243    243    243    239    219    200    189
##    [9,]    243    243    243    243    243    240    214    200    188
##   [10,]    243    243    243    243    243    243    233    207    188
##   [11,]    244    244    244    243    243    243    240    216    197
##   [12,]    249    246    245    243    243    243    243    214    207
##   [13,]    260    252    247    243    243    243    242    216    204
##   [14,]    275    262    252    243    243    243    242    218    208
##   [15,]    285    270    258    247    243    243    241    221    214
##   [16,]    281    271    262    248    243    243    239    225    220
##   [17,]    263    261    259    255    243    243    236    221    222
##   [18,]    247    250    259    265    253    243    223    182    202
##   [19,]    243    245    264    278    263    250    243    182    182
##   [20,]    232    243    281    300    278    256    243    182    182
##   [21,]    222    243    304    304    304    257    243    182    183
##   [22,]    204    223    243    294    274    233    195    188    183
##   [23,]    182    202    221    243    223    182    188    181    186
##   [24,]    157    171    192    194    176    174    175    177    179
##   [25,]    134    132    143    153    153    160    160    165    170
##   [26,]     91     80    101    116    133    136    134    135    139
##   [27,]     62     60     60     91    121    121     92     91    111
##   [28,]     60     60     60     60     71     63     61     60     76
##   [29,]     73     60     60     60     60     60     61     60     60
##   [30,]     85     84     66     60     60     60     60     60     60
##   [31,]    107    112    108     93     79     72     65     60     60
##   [32,]    121    138    137    121    106    103     89     84     81
##   [33,]    170    170    171    149    135    126    113    112    112
##   [34,]    208    213    204    182    166    151    145    138    137
##   [35,]    237    242    238    225    197    175    173    162    160
##   [36,]    238    243    243    243    243    212    194    182    182
##   [37,]    241    242    243    243    237    233    228    229    228
##   [38,]    242    243    243    243    243    243    243    242    243
##   [39,]    243    243    243    243    243    243    243    243    243
##   [40,]    243    243    243    243    243    243    243    243    243
##   [41,]    243    243    243    243    243    243    243    243    243
##   [42,]    243    243    243    243    243    243    243    243    243
##   [43,]    243    243    243    243    243    243    243    243    243
##   [44,]    243    243    243    243    243    243    243    243    243
##   [45,]    243    243    243    243    243    243    243    243    243
##   [46,]    244    243    243    243    243    243    243    243    243
##   [47,]    249    243    243    243    243    243    243    243    243
##   [48,]    246    245    243    243    243    243    243    243    243
##   [49,]    259    243    244    243    243    243    243    243    243
##   [50,]    267    243    243    244    243    243    243    243    243
##   [51,]    259    243    243    243    243    243    243    243    243
##   [52,]    254    243    244    243    243    243    243    243    243
##   [53,]    244    245    244    243    243    243    243    243    243
##   [54,]    243    244    244    243    243    243    243    243    243
##   [55,]    243    243    243    243    243    243    243    243    243
##   [56,]    243    243    243    243    243    243    243    243    243
##   [57,]    243    243    243    243    243    243    243    243    243
##   [58,]    274    250    243    243    243    243    243    243    243
##   [59,]    302    285    268    256    254    253    253    249    243
##   [60,]    310    306    304    287    285    284    284    279    249
##   [61,]    320    327    316    304    304    304    304    304    254
##   [62,]    332    349    352    329    304    304    304    288    265
##   [63,]    339    360    361    365    335    304    304    295    282
##   [64,]    346    365    365    364    365    350    323    315    303
##   [65,]    341    358    365    365    365    365    365    340    314
##   [66,]    329    344    361    365    365    365    365    360    331
##   [67,]    314    329    349    359    365    365    365    365    365
##   [68,]    304    314    342    353    359    364    365    365    365
##   [69,]    303    304    338    349    356    362    364    365    365
##   [70,]    304    318    337    347    355    362    365    365    365
##   [71,]    319    333    341    350    357    365    364    365    369
##   [72,]    330    344    350    354    359    362    365    365    373
##   [73,]    348    360    360    361    363    364    364    365    380
##   [74,]    365    366    365    364    364    365    365    375    391
##   [75,]    367    373    377    374    375    378    385    396    405
##   [76,]    371    387    395    398    405    409    410    420    426
##   [77,]    375    400    418    421    426    427    423    431    437
##   [78,]    386    407    416    426    431    431    436    443    450
##   [79,]    394    411    419    426    436    440    445    454    462
##   [80,]    409    426    426    436    443    449    455    463    473
##   [81,]    417    425    434    443    451    459    464    471    479
##   [82,]    417    426    441    452    462    472    473    477    483
##   [83,]    419    426    447    463    475    487    480    482    487
##         [,470] [,471] [,472] [,473] [,474] [,475] [,476] [,477] [,478]
##    [1,]    123    114    103     94     88     76     67     62     58
##    [2,]    131    120    109    102     95     81     71     64     59
##    [3,]    132    120    112    109    100     92     77     69     61
##    [4,]    136    129    135    122    117    104     95     80     69
##    [5,]    164    163    164    147    135    122    113     99     80
##    [6,]    174    177    179    172    162    144    128    115    100
##    [7,]    183    181    180    179    166    152    134    122    110
##    [8,]    183    177    172    168    153    142    124    112    111
##    [9,]    177    165    158    147    140    130    102     87     87
##   [10,]    170    147    137    137    132    117     98     79     71
##   [11,]    180    166    151    138    133    127    112     94     84
##   [12,]    195    181    182    161    149    138    129    121    105
##   [13,]    198    191    188    185    174    162    151    138    126
##   [14,]    203    201    200    196    190    182    170    154    138
##   [15,]    211    210    212    210    205    198    188    168    148
##   [16,]    219    220    224    224    222    218    210    179    161
##   [17,]    224    234    243    243    243    243    243    212    177
##   [18,]    212    225    243    243    243    243    243    243    201
##   [19,]    196    212    229    243    241    243    243    243    208
##   [20,]    185    191    206    219    232    238    243    233    192
##   [21,]    182    182    182    208    225    233    243    196    179
##   [22,]    182    182    197    212    230    225    210    192    167
##   [23,]    183    197    213    233    243    213    198    186    159
##   [24,]    189    210    236    241    243    192    182    170    152
##   [25,]    187    203    215    243    182    185    170    160    147
##   [26,]    175    184    186    175    172    162    157    149    139
##   [27,]    131    150    158    155    151    148    144    137    128
##   [28,]    112    104    136    136    137    135    133    127    121
##   [29,]     60     60    121    121    125    126    125    123    102
##   [30,]     60     60     60     60    121    121    121    109     85
##   [31,]     60     60     60     60     60     76     76     72     63
##   [32,]     75     60     60     60     60     60     60     60     60
##   [33,]    104     93     79     72     66     60     60     60     60
##   [34,]    126    121    105    103     97     94     81     81     81
##   [35,]    154    145    134    130    128    124    112    111    111
##   [36,]    182    182    165    155    147    138    130    122    121
##   [37,]    228    223    196    176    164    153    140    122    121
##   [38,]    243    243    243    200    182    170    158    147    134
##   [39,]    243    242    215    208    193    182    174    164    158
##   [40,]    242    238    218    204    197    190    184    182    182
##   [41,]    242    235    220    209    200    192    185    182    182
##   [42,]    239    230    223    213    204    194    183    182    182
##   [43,]    235    228    221    214    206    196    182    182    182
##   [44,]    236    230    225    220    216    206    192    182    182
##   [45,]    239    235    232    232    231    219    203    191    182
##   [46,]    243    242    242    243    243    231    214    205    198
##   [47,]    243    243    243    243    243    243    225    220    214
##   [48,]    243    243    243    243    243    240    237    237    236
##   [49,]    243    243    243    243    243    243    243    242    243
##   [50,]    243    243    243    243    243    243    243    243    243
##   [51,]    243    243    243    243    243    243    243    243    243
##   [52,]    243    243    243    243    243    243    243    243    243
##   [53,]    243    243    243    243    243    243    243    243    243
##   [54,]    243    243    243    243    243    243    243    243    243
##   [55,]    243    243    243    243    243    243    243    243    243
##   [56,]    243    243    243    243    243    243    243    243    243
##   [57,]    243    243    243    243    243    243    243    243    243
##   [58,]    243    243    243    243    243    243    243    243    243
##   [59,]    243    243    243    243    243    243    243    243    243
##   [60,]    243    243    243    243    243    243    243    243    243
##   [61,]    243    243    243    243    243    243    243    243    243
##   [62,]    243    243    243    243    243    243    243    243    243
##   [63,]    260    243    243    243    243    243    243    243    243
##   [64,]    279    258    243    243    243    243    243    243    243
##   [65,]    304    271    243    243    243    243    243    243    243
##   [66,]    304    287    270    257    256    249    243    243    243
##   [67,]    336    304    289    282    272    258    243    243    243
##   [68,]    365    340    315    299    288    273    259    249    243
##   [69,]    366    365    340    322    304    289    276    268    270
##   [70,]    368    367    359    343    328    306    294    290    290
##   [71,]    374    374    371    365    350    333    304    304    304
##   [72,]    379    381    378    373    365    355    339    335    325
##   [73,]    389    392    392    391    390    379    373    369    356
##   [74,]    399    404    408    411    411    404    397    391    377
##   [75,]    411    416    422    430    433    425    419    417    402
##   [76,]    426    426    438    445    452    456    448    435    426
##   [77,]    440    446    454    463    477    485    478    463    444
##   [78,]    454    462    470    478    487    488    487    487    462
##   [79,]    469    475    483    489    493    492    491    487    474
##   [80,]    480    487    489    495    501    500    501    496    487
##   [81,]    487    486    494    501    509    514    517    515    500
##   [82,]    487    487    499    508    520    530    535    538    529
##   [83,]    490    487    503    513    527    540    548    548    548
##         [,479] [,480] [,481] [,482] [,483] [,484] [,485] [,486] [,487]
##    [1,]     56     59     67     76     84     90     92     89     84
##    [2,]     55     58     65     72     79     85     87     84     79
##    [3,]     56     59     63     70     77     82     84     79     72
##    [4,]     61     60     62     66     70     75     77     74     68
##    [5,]     70     64     63     63     65     68     70     67     64
##    [6,]     84     72     67     64     63     63     64     63     62
##    [7,]     98     83     73     66     62     61     61     61     60
##    [8,]    103     87     76     68     63     61     60     60     60
##    [9,]     88     77     70     65     62     60     60     60     60
##   [10,]     72     72     69     66     63     61     60     60     60
##   [11,]     81     85     78     72     67     62     60     60     60
##   [12,]    103    101    101     88     75     63     60     60     60
##   [13,]    123    122    121    113     89     66     60     60     60
##   [14,]    130    123    121    103     91     60     61     60     60
##   [15,]    135    121    121    110     95     75     60     60     60
##   [16,]    147    135    121    121    110     89     69     60     60
##   [17,]    164    152    141    130    123     99     74     60     60
##   [18,]    182    170    153    139    129    113     87     67     60
##   [19,]    188    182    158    143    132    123    107     79     68
##   [20,]    179    164    154    144    134    124    108     81     69
##   [21,]    166    156    145    137    131    122     96     75     68
##   [22,]    153    139    128    129    124    111     71     63     61
##   [23,]    141    121    125    121    108     81     60     60     61
##   [24,]    138    130    123    122     82     62     62     61     60
##   [25,]    138    128    121    100     73     60     61     60     60
##   [26,]    131    124    112     94     70     62     61     60     60
##   [27,]    121    108     94     78     62     60     62     60     60
##   [28,]    108     96     84     71     60     61     60     60     60
##   [29,]     90     78     66     62     62     60     60     60     60
##   [30,]     72     60     63     60     61     61     60     60     60
##   [31,]     61     62     61     61     61     61     60     60     60
##   [32,]     62     61     60     64     62     61     60     60     60
##   [33,]     60     61     68     67     66     63     60     64     69
##   [34,]     81     82     82     79     73     69     71     73     74
##   [35,]    111    103     94     89     83     78     79     82     80
##   [36,]    121    121    103     98     91     86     88     90     87
##   [37,]    121    112    109    105     99     95     96     98     96
##   [38,]    121    121    116    112    107    104    105    106    106
##   [39,]    146    130    121    117    112    110    110    111    114
##   [40,]    174    156    134    121    119    118    118    119    121
##   [41,]    182    182    145    121    121    121    121    121    123
##   [42,]    182    163    148    121    121    121    121    121    127
##   [43,]    182    167    154    142    121    121    121    121    132
##   [44,]    182    178    172    175    143    128    121    133    138
##   [45,]    182    182    182    182    182    161    152    150    146
##   [46,]    192    182    182    182    182    182    176    163    154
##   [47,]    209    196    182    182    182    182    182    182    170
##   [48,]    234    219    205    186    182    182    182    182    177
##   [49,]    243    243    228    203    182    182    182    182    172
##   [50,]    243    243    243    216    207    192    182    182    171
##   [51,]    243    243    239    235    234    219    204    189    178
##   [52,]    243    243    243    243    243    243    228    210    195
##   [53,]    243    243    243    243    243    243    243    227    212
##   [54,]    243    243    243    243    243    243    243    243    227
##   [55,]    243    243    243    243    243    243    243    243    240
##   [56,]    243    243    243    243    243    243    243    243    243
##   [57,]    243    243    243    243    243    243    243    243    243
##   [58,]    243    243    243    243    243    243    243    243    243
##   [59,]    243    243    243    243    243    243    243    243    224
##   [60,]    243    243    243    243    243    243    243    243    225
##   [61,]    243    243    243    243    243    243    243    243    229
##   [62,]    243    243    243    243    243    243    243    243    235
##   [63,]    243    243    243    243    243    243    243    243    243
##   [64,]    243    243    243    243    243    243    243    243    243
##   [65,]    243    243    243    243    243    243    243    243    250
##   [66,]    243    243    247    247    247    247    248    253    257
##   [67,]    243    243    261    261    258    257    259    262    265
##   [68,]    252    264    277    272    268    266    268    270    273
##   [69,]    273    282    293    282    277    276    277    278    281
##   [70,]    293    299    303    288    283    282    283    284    285
##   [71,]    304    304    305    296    292    291    291    292    293
##   [72,]    321    311    305    304    301    299    299    298    298
##   [73,]    340    327    309    304    304    303    302    302    302
##   [74,]    365    346    315    304    304    304    304    304    304
##   [75,]    387    373    336    304    304    304    309    310    307
##   [76,]    411    395    372    304    304    328    321    323    315
##   [77,]    431    418    389    371    335    355    354    353    336
##   [78,]    442    426    404    387    383    379    380    373    355
##   [79,]    455    437    417    404    401    400    403    399    387
##   [80,]    473    465    436    422    420    420    426    426    426
##   [81,]    487    487    460    426    426    426    487    457    441
##   [82,]    534    513    496    475    472    487    490    495    470
##   [83,]    551    548    524    503    487    512    528    548    497
##         [,488] [,489] [,490] [,491] [,492] [,493] [,494] [,495] [,496]
##    [1,]     80     80     88     99    112    126    141    156    169
##    [2,]     75     77     89    103    115    127    141    158    175
##    [3,]     67     75     92    110    117    128    144    168    189
##    [4,]     65     73     87    101    113    125    142    160    176
##    [5,]     62     69     85    100    113    127    141    155    168
##    [6,]     61     70     85    100    113    124    136    149    162
##    [7,]     61     71     87    101    112    119    127    137    149
##    [8,]     61     71     87    100    109    111    113    122    133
##    [9,]     60     60     74     93    108    101     98    104    116
##   [10,]     60     60     66     79     83     73     76     85    100
##   [11,]     60     60     61     66     73     67     65     71     82
##   [12,]     60     60     60     60     60     61     60     60     74
##   [13,]     60     60     60     60     60     60     60     60     64
##   [14,]     60     60     60     60     60     60     60     60     60
##   [15,]     60     60     60     60     60     60     60     60     60
##   [16,]     60     60     60     60     60     60     60     60     60
##   [17,]     60     60     60     60     60     60     60     60     60
##   [18,]     60     60     60     60     60     60     60     60     60
##   [19,]     60     60     60     60     60     60     60     60     60
##   [20,]     64     61     60     60     60     60     60     60     60
##   [21,]     63     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     60     60     60     60     60     60     60     60     60
##   [24,]     60     60     60     60     60     60     60     63     75
##   [25,]     60     60     60     60     60     60     60     69     97
##   [26,]     60     60     60     60     60     60     60     68    102
##   [27,]     60     60     60     60     60     60     60     69     95
##   [28,]     60     60     60     60     60     60     60     60     90
##   [29,]     60     60     60     60     60     60     60     60     83
##   [30,]     60     60     60     60     60     60     60     60     81
##   [31,]     62     62     61     60     60     60     60     63     89
##   [32,]     64     64     62     61     60     60     60     60    101
##   [33,]     67     66     64     62     60     60     60     60     67
##   [34,]     72     70     67     64     62     60     60     60     60
##   [35,]     77     73     69     67     64     60     60     60     67
##   [36,]     84     80     75     72     68     60     60     60     80
##   [37,]     93     89     86     84     82     77     74     83     94
##   [38,]    104    101     99     98     99     97    101    107    114
##   [39,]    112    110    109    110    111    112    113    121    152
##   [40,]    120    118    118    119    121    121    131    171    182
##   [41,]    122    121    121    121    121    121    121    148    182
##   [42,]    126    123    121    121    121    121    121    131    170
##   [43,]    131    126    122    121    121    121    126    141    163
##   [44,]    135    128    122    122    121    123    131    141    161
##   [45,]    140    129    122    121    121    125    132    140    158
##   [46,]    144    129    122    121    121    124    126    126    165
##   [47,]    153    134    121    122    121    121    121    131    182
##   [48,]    162    140    124    121    121    121    121    121    182
##   [49,]    160    143    126    121    121    121    121    132    153
##   [50,]    160    139    121    123    121    121    121    126    144
##   [51,]    165    144    122    121    122    121    121    121    127
##   [52,]    182    180    182    152    142    131    121    121    121
##   [53,]    198    186    183    182    173    158    136    123    121
##   [54,]    211    193    183    182    182    182    147    129    121
##   [55,]    221    193    182    180    178    162    148    131    122
##   [56,]    216    182    178    175    167    156    143    126    122
##   [57,]    217    182    174    168    159    149    127    122    121
##   [58,]    197    182    176    170    164    161    150    121    121
##   [59,]    197    182    182    180    178    182    182    182    182
##   [60,]    205    188    182    182    190    197    201    205    196
##   [61,]    214    203    201    204    209    217    220    227    217
##   [62,]    226    219    221    225    229    236    239    248    237
##   [63,]    239    237    237    243    243    252    263    268    255
##   [64,]    245    247    249    255    265    273    284    295    280
##   [65,]    252    256    263    272    280    290    304    302    304
##   [66,]    259    267    274    282    290    300    304    304    298
##   [67,]    267    275    283    290    297    300    304    304    293
##   [68,]    275    282    289    295    300    302    303    304    294
##   [69,]    282    288    294    299    302    303    304    304    297
##   [70,]    287    292    296    300    303    304    304    304    300
##   [71,]    294    296    299    303    305    304    304    304    304
##   [72,]    299    301    304    303    313    324    308    304    304
##   [73,]    302    302    304    304    329    354    328    304    304
##   [74,]    303    303    304    304    338    365    355    325    304
##   [75,]    304    304    304    331    355    370    378    355    335
##   [76,]    304    304    304    335    365    389    418    393    365
##   [77,]    312    304    304    336    365    396    427    429    411
##   [78,]    332    304    331    341    365    397    434    448    437
##   [79,]    372    356    353    359    365    402    443    477    462
##   [80,]    404    399    387    377    365    426    469    483    487
##   [81,]    426    426    409    401    410    426    473    494    491
##   [82,]    453    444    438    436    440    451    477    506    512
##   [83,]    474    470    468    467    471    476    502    523    536
##         [,497] [,498] [,499] [,500] [,501] [,502] [,503] [,504] [,505]
##    [1,]    178    183    180    172    160    146    133    119    106
##    [2,]    186    189    184    175    162    146    128    111     98
##    [3,]    200    194    187    174    156    139    115     98     87
##    [4,]    188    189    177    163    144    123    103     89     80
##    [5,]    179    183    179    166    148    129    108     90     79
##    [6,]    172    177    179    173    161    142    120     99     84
##    [7,]    159    167    172    171    163    151    132    112     94
##    [8,]    144    156    160    161    155    146    130    111     93
##    [9,]    128    139    146    147    142    137    125    100     80
##   [10,]    113    124    126    126    122    121    116     98     79
##   [11,]     99    110    109    105    101    103    106     94     81
##   [12,]     84     96     92     85     77     79     93     90     80
##   [13,]     70     75     73     66     62     60     68     69     67
##   [14,]     61     62     60     62     60     61     60     61     60
##   [15,]     60     60     60     60     60     60     60     60     60
##   [16,]     60     60     60     60     60     60     60     60     60
##   [17,]     60     60     60     60     60     60     60     60     60
##   [18,]     60     60     60     60     60     60     60     60     60
##   [19,]     60     60     60     60     60     60     60     60     60
##   [20,]     60     60     60     60     60     60     60     60     60
##   [21,]     60     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     72     68     60     60     60     60     60     60     60
##   [24,]     91     94     81     77     70     74     69     64     60
##   [25,]    121    121    105    119     97    117     94     81     69
##   [26,]    120    128    142    166    116    148    109     94     81
##   [27,]    121    142    182    176    182    172    139    114     97
##   [28,]    110    121    148    182    180    182    149    126    121
##   [29,]    105    114    121    149    182    165    145    125    116
##   [30,]    103    113    118    121    136    154    131    124    108
##   [31,]    114    118    120    140    142    147    140    121    112
##   [32,]    117    127    145    162    182    182    155    133    121
##   [33,]    111    127    144    167    180    181    177    147    128
##   [34,]     93    110    121    121    152    182    182    164    142
##   [35,]     97    110    118    121    121    182    182    171    156
##   [36,]    103    114    121    121    121    182    187    182    170
##   [37,]    109    121    182    182    182    206    205    197    182
##   [38,]    152    192    220    228    231    238    235    231    217
##   [39,]    192    243    233    249    251    252    263    255    243
##   [40,]    208    235    243    261    277    292    294    291    271
##   [41,]    203    223    243    273    304    302    304    304    304
##   [42,]    188    218    243    267    294    304    304    304    304
##   [43,]    182    210    243    255    279    304    304    304    304
##   [44,]    182    199    224    243    261    290    304    296    282
##   [45,]    178    182    221    236    243    276    280    277    265
##   [46,]    190    212    233    243    251    265    264    256    249
##   [47,]    202    228    243    249    252    273    252    243    230
##   [48,]    202    243    241    243    245    245    243    228    218
##   [49,]    172    196    224    228    228    220    209    207    199
##   [50,]    153    166    182    182    182    182    182    188    182
##   [51,]    130    145    151    154    152    155    168    171    162
##   [52,]    121    121    128    129    121    128    147    146    143
##   [53,]    117    112    109    103    105    115    128    130    127
##   [54,]    113     94     76     60     82    107    121    121     82
##   [55,]    112     89     60     63     61     60     60     60     60
##   [56,]    105     90     79     60     60     60     60     60     60
##   [57,]    111    104     92     82     68     60     60     60     60
##   [58,]    121    121    109    104     83     60     60     60     60
##   [59,]    152    134    121    121     98     75     60     60     60
##   [60,]    187    171    156    141    121     98     88     83     82
##   [61,]    206    194    182    167    142    121    108    103    104
##   [62,]    225    213    200    188    163    132    121    118    116
##   [63,]    243    231    219    206    188    162    149    121    121
##   [64,]    262    249    237    225    208    195    189    185    167
##   [65,]    279    263    251    243    228    224    210    197    182
##   [66,]    287    272    259    250    248    245    235    220    205
##   [67,]    283    275    267    263    261    257    250    243    228
##   [68,]    286    280    275    274    274    271    266    259    243
##   [69,]    291    288    285    287    287    285    281    277    263
##   [70,]    296    294    293    295    295    294    293    290    287
##   [71,]    303    302    302    304    305    309    311    310    307
##   [72,]    304    304    304    304    306    322    332    326    318
##   [73,]    304    304    304    304    309    340    357    344    333
##   [74,]    304    304    304    304    304    365    359    365    352
##   [75,]    314    304    304    304    304    365    365    370    370
##   [76,]    345    324    304    304    304    365    365    382    390
##   [77,]    380    355    335    322    327    345    365    400    419
##   [78,]    426    395    365    365    353    353    365    426    442
##   [79,]    448    435    415    392    363    360    365    426    457
##   [80,]    472    464    452    405    375    364    385    426    458
##   [81,]    487    487    487    441    406    410    426    441    462
##   [82,]    518    518    511    496    457    423    439    461    479
##   [83,]    548    548    548    523    500    487    467    487    521
##         [,506] [,507] [,508] [,509] [,510] [,511] [,512] [,513] [,514]
##    [1,]     94     84     76     68     63     59     57     57     58
##    [2,]     88     80     72     66     61     58     57     58     60
##    [3,]     80     74     68     63     59     57     58     60     61
##    [4,]     74     70     65     61     58     57     58     60     60
##    [5,]     72     67     63     61     59     58     59     60     60
##    [6,]     74     68     63     61     60     59     60     60     60
##    [7,]     80     71     64     61     61     60     60     60     60
##    [8,]     79     70     64     61     61     60     60     60     61
##    [9,]     70     65     62     61     61     60     60     60     62
##   [10,]     69     64     62     62     61     60     60     60     60
##   [11,]     69     63     61     61     61     60     60     60     60
##   [12,]     68     60     60     60     60     60     60     60     60
##   [13,]     62     62     61     60     60     60     60     60     60
##   [14,]     60     61     60     60     60     60     60     60     60
##   [15,]     60     60     60     60     60     60     60     60     60
##   [16,]     60     60     60     60     60     60     60     60     60
##   [17,]     60     60     60     60     60     60     60     60     60
##   [18,]     60     60     60     60     60     60     60     60     60
##   [19,]     60     60     60     60     60     60     60     60     60
##   [20,]     60     60     60     60     60     60     60     60     60
##   [21,]     60     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     60     60     60     60     60     60     60     60     60
##   [24,]     60     60     60     60     60     60     60     60     60
##   [25,]     60     60     60     60     60     60     60     60     60
##   [26,]     68     60     60     60     60     60     60     60     60
##   [27,]     77     60     60     60     60     60     60     60     60
##   [28,]     91     73     60     60     60     60     60     60     60
##   [29,]     99     78     60     60     60     60     60     60     60
##   [30,]     94     79     60     60     60     60     60     60     60
##   [31,]     97     82     67     60     60     60     60     60     60
##   [32,]    106     92     80     65     60     60     60     60     60
##   [33,]    118    104     92     76     60     60     60     60     60
##   [34,]    121    115    104     87     72     60     60     60     60
##   [35,]    145    129    117    102     89     81     73     67     63
##   [36,]    166    151    137    116    108    104     98     84     68
##   [37,]    182    167    152    129    121    121    110     90     71
##   [38,]    202    189    175    154    135    126    121     94     65
##   [39,]    227    212    194    175    148    133    121    100     79
##   [40,]    252    236    208    180    157    138    125    115     85
##   [41,]    277    243    223    176    156    143    128    121     90
##   [42,]    304    268    243    177    155    138    121    104     87
##   [43,]    280    267    243    197    158    139    121    106     89
##   [44,]    268    249    233    194    161    140    121    105     90
##   [45,]    254    243    209    179    158    140    121    104     87
##   [46,]    234    215    192    171    151    137    121     99     83
##   [47,]    216    200    182    162    144    130    121     90     67
##   [48,]    206    193    182    158    138    121    108     88     60
##   [49,]    188    178    163    146    134    124    115     79     60
##   [50,]    172    164    153    141    133    125    121     60     69
##   [51,]    156    150    141    132    125     91     68     70     66
##   [52,]    141    136    129    121     60     74     64     68     64
##   [53,]    126    125     91     67     67     62     64     63     63
##   [54,]     60     60     69     61     62     61     61     61     61
##   [55,]     63     61     61     61     61     61     61     61     63
##   [56,]     60     60     60     60     61     60     60     60     69
##   [57,]     60     60     60     60     60     60     60     60     60
##   [58,]     60     60     60     60     60     60     60     60     60
##   [59,]     60     60     60     60     60     60     60     60     60
##   [60,]     83     85     86     73     64     60     60     60     60
##   [61,]    106    111    112     90     76     60     60     60     60
##   [62,]    117    120    120    113     96     78     60     60     65
##   [63,]    121    121    121    122    121    101     78     60     81
##   [64,]    142    128    123    125    123    121     97     97    100
##   [65,]    170    153    144    133    128    121    111    112    114
##   [66,]    190    175    169    151    139    129    121    119    118
##   [67,]    213    203    186    170    153    139    129    121    121
##   [68,]    228    216    196    182    162    146    134    125    121
##   [69,]    250    236    209    182    168    153    138    123    122
##   [70,]    271    249    210    182    168    155    140    121    121
##   [71,]    295    263    233    182    172    163    153    132    121
##   [72,]    310    288    243    223    182    182    182    162    149
##   [73,]    322    304    276    254    233    228    208    195    189
##   [74,]    340    327    304    284    279    256    243    226    212
##   [75,]    359    355    348    323    311    293    272    253    236
##   [76,]    398    391    377    365    344    329    304    284    272
##   [77,]    434    427    414    393    378    370    349    335    305
##   [78,]    467    474    439    426    409    395    385    372    348
##   [79,]    487    485    466    444    426    411    400    386    370
##   [80,]    487    500    494    477    456    435    420    403    386
##   [81,]    487    520    523    505    487    460    426    412    396
##   [82,]    505    544    550    537    517    497    472    431    411
##   [83,]    548    561    562    556    548    528    507    472    426
##         [,515] [,516] [,517] [,518] [,519] [,520] [,521] [,522] [,523]
##    [1,]     60     63     69     76     86     96    106    116    120
##    [2,]     62     64     68     74     82     94    107    118    124
##    [3,]     62     63     68     70     78     95    114    124    129
##    [4,]     61     63     66     70     79     97    113    124    132
##    [5,]     61     63     67     72     84    100    115    127    135
##    [6,]     62     66     72     80     91    103    116    130    140
##    [7,]     64     71     80     89     98    106    119    134    145
##    [8,]     66     77     89     99    107    112    122    135    149
##    [9,]     65     79    100    112    115    117    119    125    139
##   [10,]     61     73     97    111    115    117    117    120    127
##   [11,]     60     64     80     97    107    111    108    113    121
##   [12,]     60     60     65     83     94     95     96    101    121
##   [13,]     60     60     60     66     72     72     66     62     78
##   [14,]     60     60     60     60     60     62     60     60     61
##   [15,]     60     60     60     60     60     60     61     60     60
##   [16,]     60     60     60     60     60     60     60     60     60
##   [17,]     60     60     60     60     60     60     60     60     60
##   [18,]     60     60     60     60     60     60     60     60     60
##   [19,]     60     60     60     60     60     60     60     60     60
##   [20,]     60     60     60     60     60     60     60     60     60
##   [21,]     60     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     60     60     60     60     60     60     60     60     60
##   [24,]     60     60     60     60     60     60     60     60     60
##   [25,]     60     60     60     60     60     60     60     60     60
##   [26,]     60     60     60     60     60     60     60     60     60
##   [27,]     60     60     60     60     60     60     60     60     60
##   [28,]     60     60     60     60     60     60     60     60     60
##   [29,]     60     60     60     60     60     60     60     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     60     60     60     60     60     60     60     60     60
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     60     60     60     60
##   [34,]     60     60     60     60     60     60     60     60     60
##   [35,]     60     60     60     60     60     60     60     60     60
##   [36,]     62     60     60     60     60     60     60     60     60
##   [37,]     62     61     60     60     60     60     60     60     60
##   [38,]     62     60     60     60     60     60     60     60     60
##   [39,]     61     60     60     60     60     60     60     60     60
##   [40,]     63     60     60     60     60     60     60     60     60
##   [41,]     65     60     60     60     60     60     60     60     60
##   [42,]     64     61     61     60     60     60     60     60     60
##   [43,]     67     60     60     60     60     60     60     60     60
##   [44,]     68     60     60     60     60     60     60     60     60
##   [45,]     67     60     60     60     60     60     60     60     60
##   [46,]     65     60     60     60     60     60     60     60     60
##   [47,]     61     61     60     60     60     60     60     60     60
##   [48,]     61     60     60     60     60     60     60     60     60
##   [49,]     61     60     60     60     60     60     60     60     60
##   [50,]     62     60     60     60     71     74     75     72     60
##   [51,]     63     60     68     80     88     97     98     94     81
##   [52,]     62     73     85     98    109    121    121    121    105
##   [53,]     61     85    102    115    128    142    161    162    135
##   [54,]     73    101    121    132    149    167    180    182    182
##   [55,]     90    121    131    145    161    182    181    182    182
##   [56,]     93    121    136    150    163    182    182    182    182
##   [57,]     92    121    135    148    162    182    182    162    152
##   [58,]     87    121    130    138    147    156    155    131    116
##   [59,]     77    113    121    124    127    130    126    108     91
##   [60,]     80    121    119    120    121    122    122     87     68
##   [61,]     89    105    121    121    121    121    106     60     69
##   [62,]     87    103    115    121    121    121    103     60     61
##   [63,]     99    109    121    119    121    121     71     64     61
##   [64,]    115    120    119    120    121     93     66     62     61
##   [65,]    121    121    121    121    114     98     77     60     61
##   [66,]    119    121    123    121    113    103     83     60     60
##   [67,]    121    121    130    130    121    111     93     75     60
##   [68,]    121    121    138    143    136    121    103     85     78
##   [69,]    121    131    157    172    170    150    123    103     95
##   [70,]    121    121    182    178    182    182    151    121    111
##   [71,]    121    121    182    182    182    188    176    152    139
##   [72,]    121    155    159    182    182    201    197    182    182
##   [73,]    172    170    178    181    182    224    231    213    196
##   [74,]    205    203    192    182    214    241    243    243    222
##   [75,]    234    233    218    218    223    238    242    243    243
##   [76,]    260    252    243    236    235    240    243    243    243
##   [77,]    284    278    263    249    242    242    243    243    243
##   [78,]    304    304    285    266    243    243    245    243    219
##   [79,]    341    324    304    284    264    247    248    243    231
##   [80,]    372    368    348    319    294    277    262    253    246
##   [81,]    389    382    372    365    329    299    277    264    253
##   [82,]    404    399    386    371    358    315    288    272    258
##   [83,]    426    426    406    385    365    321    291    275    257
##         [,524] [,525] [,526] [,527] [,528] [,529] [,530] [,531] [,532]
##    [1,]    116    110    101     92     83     74     68     62     57
##    [2,]    123    118    109    100     90     80     72     67     63
##    [3,]    129    124    114    103     92     83     76     71     67
##    [4,]    133    128    118    107     95     88     81     75     69
##    [5,]    138    135    126    117    107     97     88     81     74
##    [6,]    145    145    138    131    122    112    101     91     85
##    [7,]    152    153    150    146    139    132    122    110     99
##    [8,]    156    161    159    158    156    153    142    130    119
##    [9,]    154    168    167    167    173    175    164    149    137
##   [10,]    129    140    152    156    170    170    166    154    141
##   [11,]    124    120    122    134    145    160    158    143    134
##   [12,]    121     97     91    101    121    121    121    121    121
##   [13,]     81     71     64     65     62     60     91    100    114
##   [14,]     60     63     60     62     60     61     60     69     93
##   [15,]     60     60     61     60     60     60     60     60     78
##   [16,]     60     60     60     60     60     60     60     64     67
##   [17,]     60     60     60     60     60     60     60     60     60
##   [18,]     60     60     60     60     60     60     60     60     60
##   [19,]     60     60     60     60     60     60     60     60     60
##   [20,]     60     60     60     60     60     60     60     60     60
##   [21,]     60     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     79
##   [23,]     60     60     60     60     60     60     60     60     89
##   [24,]     60     60     60     60     60     60     60     60     86
##   [25,]     60     60     60     60     60     60     60     65     71
##   [26,]     60     60     60     60     60     60     60     60     60
##   [27,]     60     60     60     60     60     60     60     60     60
##   [28,]     60     60     60     60     60     60     60     60     60
##   [29,]     60     60     60     60     60     60     60     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     60     60     60     60     60     60     60     60     60
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     60     60     60     60
##   [34,]     60     60     60     60     60     60     60     60     60
##   [35,]     60     60     60     60     60     60     60     60     60
##   [36,]     60     60     60     60     60     60     60     60     60
##   [37,]     60     60     60     60     60     60     60     60     60
##   [38,]     60     60     60     60     60     60     60     60     60
##   [39,]     60     60     60     60     60     60     60     60     60
##   [40,]     60     60     60     60     60     60     60     60     60
##   [41,]     60     60     60     60     60     60     60     60     60
##   [42,]     60     60     60     60     60     60     60     60     60
##   [43,]     60     60     60     60     60     60     60     60     60
##   [44,]     60     60     60     60     60     60     60     60     60
##   [45,]     60     60     60     60     60     60     60     60     60
##   [46,]     60     60     60     60     60     60     60     60     60
##   [47,]     60     60     60     60     60     60     60     60     60
##   [48,]     60     60     60     60     60     60     60     60     60
##   [49,]     60     60     60     60     60     60     60     60     60
##   [50,]     60     60     60     60     60     60     60     60     60
##   [51,]     67     60     60     60     60     60     60     60     60
##   [52,]     90     75     60     60     60     60     60     60     60
##   [53,]    114     98     94     92     91     91     84     73     65
##   [54,]    151    121    121    121    121    121    121    104     89
##   [55,]    182    182    167    133    123    121    121    121    106
##   [56,]    182    182    148    137    123    121    121    121    121
##   [57,]    152    145    145    130    121    121    121    121    121
##   [58,]    110    106    101     91     76     76     76     76     76
##   [59,]     77     60     60     65     60     60     60     60     60
##   [60,]     63     63     61     60     60     60     60     60     60
##   [61,]     61     60     60     60     60     60     60     60     60
##   [62,]     62     61     60     60     60     60     60     60     60
##   [63,]     61     60     60     60     60     60     60     60     60
##   [64,]     61     60     60     60     60     60     60     60     60
##   [65,]     60     60     61     60     60     60     60     60     60
##   [66,]     60     60     65     60     60     60     60     60     60
##   [67,]     60     72     75     67     60     60     60     62     61
##   [68,]     78     80     85     80     70     60     71     68     66
##   [69,]     96     97     99     95     88     86     81     78     73
##   [70,]    111    112    112    111    107    102     97     93     86
##   [71,]    132    129    126    124    122    117    115    114    104
##   [72,]    165    151    141    131    124    122    121    121    121
##   [73,]    182    169    152    136    126    123    122    121    103
##   [74,]    189    182    160    139    127    123    121    121     81
##   [75,]    182    165    146    128    123    102     76     71     60
##   [76,]    199    156    121    121     91     60     66     61     60
##   [77,]    192    166    145    116     91     60     60     63     61
##   [78,]    193    177    162    136    109     77     60     60     60
##   [79,]    214    198    182    154    131    121     81     60     60
##   [80,]    235    215    193    170    139    121     91     60     60
##   [81,]    247    243    223    190    148    121     94     60     60
##   [82,]    248    244    222    189    162    133    111     60     60
##   [83,]    243    220    201    192    182    157    121    101     60
##         [,533] [,534] [,535] [,536] [,537] [,538] [,539] [,540] [,541]
##    [1,]     52     48     46     44     43     43     44     45     47
##    [2,]     59     55     53     51     50     49     49     49     49
##    [3,]     63     60     58     56     55     53     52     51     50
##    [4,]     65     62     60     58     57     55     54     52     51
##    [5,]     70     66     64     62     60     58     56     54     53
##    [6,]     79     74     72     69     66     62     59     57     56
##    [7,]     91     85     83     79     75     69     64     61     59
##    [8,]    108     98     94     90     85     78     71     66     63
##    [9,]    123    112    106    102     96     86     78     72     69
##   [10,]    132    124    118    113    109     99     91     85     80
##   [11,]    129    125    123    121    118    111    106     99     92
##   [12,]    122    123    122    122    121    121    121    112    104
##   [13,]    121    121    121    121    121    121    121    121    112
##   [14,]    105    115    121    121    121    121    121    121    121
##   [15,]     88     96    100    102    112    121    121    121    121
##   [16,]     71     76     78     74     85    100    113    121    121
##   [17,]     62     63     63     62     60     76     83     87     99
##   [18,]     60     61     60     60     61     60     60     60     69
##   [19,]     60     63     60     60     60     60     60     60     60
##   [20,]     60     74     76     64     60     60     60     60     60
##   [21,]     79     91    101     84     60     60     60     60     60
##   [22,]     98    114    119    103     66     60     60     60     60
##   [23,]    121    115    121    103     72     65     61     60     60
##   [24,]    121    121    121     88     70     64     61     60     60
##   [25,]     79     91     92     76     64     62     61     60     60
##   [26,]     60     62     60     62     60     60     60     60     60
##   [27,]     60     60     60     60     60     60     60     60     60
##   [28,]     60     60     60     60     60     60     60     60     60
##   [29,]     60     60     60     60     60     60     60     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     60     60     60     60     60     60     60     60     60
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     61     61     60     60
##   [34,]     60     60     60     60     60     61     63     62     60
##   [35,]     60     60     60     60     60     62     65     67     69
##   [36,]     60     60     60     60     60     64     70     74     80
##   [37,]     60     60     60     60     60     66     75     84     93
##   [38,]     60     60     60     60     60     65     74     84     92
##   [39,]     60     60     60     60     60     67     74     78     84
##   [40,]     60     60     60     60     60     62     65     68     70
##   [41,]     60     60     60     60     60     60     60     61     60
##   [42,]     60     60     60     60     60     60     60     60     60
##   [43,]     60     60     60     60     60     60     60     60     60
##   [44,]     60     60     60     60     60     60     60     60     60
##   [45,]     60     60     60     60     60     60     60     60     60
##   [46,]     60     60     60     60     60     60     60     60     60
##   [47,]     60     60     60     60     60     60     60     60     60
##   [48,]     60     60     60     60     60     60     60     60     60
##   [49,]     60     60     60     60     60     60     60     60     60
##   [50,]     60     60     60     60     60     60     60     60     60
##   [51,]     60     60     60     60     60     60     60     60     60
##   [52,]     60     60     60     60     60     60     60     60     60
##   [53,]     60     60     60     60     60     60     60     60     60
##   [54,]     84     65     60     60     60     60     60     60     60
##   [55,]    103     77     60     60     60     60     60     60     60
##   [56,]    121     93     60     60     60     60     60     60     60
##   [57,]    121     71     63     61     60     60     60     60     60
##   [58,]     71     63     61     61     60     60     60     60     60
##   [59,]     60     60     60     60     60     60     60     60     60
##   [60,]     60     60     60     60     60     60     60     60     60
##   [61,]     60     60     60     60     60     60     60     60     60
##   [62,]     60     60     60     60     60     60     60     60     60
##   [63,]     60     60     60     60     60     60     60     60     60
##   [64,]     60     60     60     60     60     60     60     60     60
##   [65,]     60     60     60     60     60     60     60     60     60
##   [66,]     60     60     60     60     60     60     60     60     60
##   [67,]     60     60     60     60     60     60     60     60     60
##   [68,]     63     60     60     60     60     60     60     60     60
##   [69,]     68     60     60     60     60     60     60     60     60
##   [70,]     81     67     60     60     60     60     60     60     60
##   [71,]    100     91     73     69     65     60     67     65     60
##   [72,]    121    121    104     94     86     89     83     77     66
##   [73,]    118    121    121    115    113    113    102     92     78
##   [74,]    116    121    122    125    128    126    121    114     96
##   [75,]    119    121    124    130    138    142    146    139    115
##   [76,]     91    121    126    138    149    161    171    182    182
##   [77,]     71    121    128    140    156    171    182    197    213
##   [78,]     60     74    121    137    160    182    182    220    243
##   [79,]     60     60    101    121    155    182    192    201    202
##   [80,]     60     74    121    133    146    159    171    173    171
##   [81,]     60     81    121    129    136    142    145    144    144
##   [82,]     60     60     84    110    123    125    127    121    126
##   [83,]     60     60     60     79    100    121    122    101     60
##         [,542] [,543] [,544] [,545] [,546] [,547] [,548] [,549] [,550]
##    [1,]     48     47     45     42     39     36     34     33     31
##    [2,]     48     47     45     43     41     40     38     36     35
##    [3,]     50     49     46     45     44     43     41     39     38
##    [4,]     51     49     47     46     45     45     43     41     39
##    [5,]     53     50     48     48     47     46     44     42     41
##    [6,]     55     52     50     50     49     48     45     44     43
##    [7,]     57     54     52     52     52     50     47     46     45
##    [8,]     60     57     55     54     54     52     49     48     47
##    [9,]     65     61     58     57     56     54     51     50     49
##   [10,]     73     66     62     59     58     55     53     52     51
##   [11,]     83     72     65     61     60     57     55     54     53
##   [12,]     94     80     68     62     60     58     56     56     55
##   [13,]    101     85     68     60     59     59     58     58     57
##   [14,]    111     92     71     63     60     60     60     60     59
##   [15,]    121    100     71     65     63     61     60     61     60
##   [16,]    121     95     68     63     62     62     64     64     62
##   [17,]     99     78     64     62     63     64     66     68     68
##   [18,]     78     68     62     61     63     65     69     74     76
##   [19,]     60     62     60     60     64     67     73     80     86
##   [20,]     60     61     61     60     65     68     71     77     83
##   [21,]     60     60     60     60     60     60     63     66     68
##   [22,]     60     60     60     60     60     60     60     62     63
##   [23,]     60     60     60     60     60     60     60     60     61
##   [24,]     60     60     60     60     60     60     60     60     60
##   [25,]     60     60     60     60     60     60     60     60     60
##   [26,]     60     60     60     60     60     60     60     60     60
##   [27,]     60     60     60     60     60     60     60     60     60
##   [28,]     60     60     60     60     60     60     60     60     60
##   [29,]     60     60     60     60     60     60     60     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     60     60     60     60     60     60     60     60     60
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     60     60     60     60
##   [34,]     60     62     60     60     60     60     60     61     60
##   [35,]     72     70     65     60     60     60     66     73     60
##   [36,]     88     89     80     69     60     60     77    108     94
##   [37,]    112    121    104     98     79     60    111    114    121
##   [38,]    108    121    121    121    111    109    119    119    121
##   [39,]     92    110    121    121    121    121    120    121     94
##   [40,]     74     98    112    121    121    121    121    110     83
##   [41,]     61     88    108    121    121    121    118     96     68
##   [42,]     65     87    116    119    121    121    118     98     73
##   [43,]     68     89     98    121    121    121    121    121    101
##   [44,]     69     77     83     93    112    121    121    121    121
##   [45,]     60     62     61     69     88    101    118    121    121
##   [46,]     60     60     60     60     70     77     97    121    121
##   [47,]     60     60     60     60     60     60     70     86     98
##   [48,]     60     60     60     60     60     60     60     60     66
##   [49,]     60     60     60     60     60     60     60     60     60
##   [50,]     60     60     60     60     60     60     60     60     60
##   [51,]     60     60     60     60     60     60     60     60     60
##   [52,]     60     60     60     60     60     60     60     60     60
##   [53,]     60     60     60     60     60     60     60     60     60
##   [54,]     60     60     60     60     60     60     60     60     60
##   [55,]     60     60     60     60     60     60     60     60     60
##   [56,]     60     60     60     60     60     60     60     60     60
##   [57,]     60     60     60     60     60     60     60     60     60
##   [58,]     60     60     60     60     60     60     60     60     60
##   [59,]     60     60     60     60     60     60     60     60     60
##   [60,]     60     60     60     60     60     60     60     60     60
##   [61,]     60     60     60     60     60     60     60     60     60
##   [62,]     60     60     60     60     60     60     60     60     60
##   [63,]     60     60     60     60     60     60     60     60     60
##   [64,]     60     60     60     60     60     60     60     60     60
##   [65,]     60     60     60     60     60     60     60     60     60
##   [66,]     60     60     60     60     60     60     60     60     60
##   [67,]     60     60     60     60     60     60     60     60     60
##   [68,]     60     60     60     60     60     60     60     60     60
##   [69,]     60     60     60     60     60     61     60     60     60
##   [70,]     60     60     60     60     60     64     60     60     60
##   [71,]     60     60     60     60     60     73     76     68     60
##   [72,]     60     60     60     60     60     85    101     96     76
##   [73,]     67     60     60     70     83     99    121    121    107
##   [74,]     88     85     87     92    103    113    121    121    121
##   [75,]    113    112    106    108    116    118    118    121    100
##   [76,]    182    182    137    129    124    121    121    103     88
##   [77,]    213    188    182    154    134    123    121     99     79
##   [78,]    225    201    182    165    139    121    105     92     76
##   [79,]    182    182    174    160    139    121    102     85     69
##   [80,]    166    156    151    143    130    112     94     75     60
##   [81,]    141    136    131    121    113     90     74     60     63
##   [82,]    125    107    101     77     81     68     62     62     61
##   [83,]     60     60     60     67     60     63     60     61     60
##         [,551] [,552] [,553] [,554] [,555] [,556] [,557] [,558] [,559]
##    [1,]     30     30     29     29     29     29     29     28     28
##    [2,]     34     33     33     33     33     33     33     33     32
##    [3,]     37     36     35     36     37     37     37     37     37
##    [4,]     39     38     37     38     39     39     39     39     39
##    [5,]     41     39     39     40     40     40     41     41     41
##    [6,]     43     41     42     42     42     43     43     43     43
##    [7,]     45     43     44     44     45     45     45     45     45
##    [8,]     47     45     46     46     47     47     47     47     47
##    [9,]     49     47     48     49     49     49     49     49     49
##   [10,]     51     49     50     51     51     51     51     51     52
##   [11,]     53     51     52     52     53     53     53     53     53
##   [12,]     55     53     54     54     55     55     55     55     55
##   [13,]     56     56     56     56     57     57     57     57     58
##   [14,]     59     58     58     58     59     59     60     60     63
##   [15,]     60     60     60     60     63     60     70     80     76
##   [16,]     60     60     60     69     74     75     87    100     99
##   [17,]     66     60     75     85     92    100    111    121    121
##   [18,]     77     82     91    101    108    119    126    132    142
##   [19,]     91     97    110    121    121    121    141    156    182
##   [20,]     88     94    103    106    115    124    140    154    166
##   [21,]     69     68     60     60     83    119    137    147    157
##   [22,]     63     60     62     60     60    123    132    140    146
##   [23,]     60     61     60     60     80    108    125    126    128
##   [24,]     60     60     60     60     70     88    121    103    111
##   [25,]     60     60     60     60     60     63     62     72     79
##   [26,]     60     60     60     60     60     60     60     61     60
##   [27,]     60     60     60     60     60     60     60     60     60
##   [28,]     60     60     60     60     60     60     60     60     60
##   [29,]     60     60     60     60     60     60     60     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     60     60     60     60     60     60     60     60     60
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     60     60     60     60
##   [34,]     60     60     60     60     60     60     60     60     60
##   [35,]     60     60     60     60     60     60     60     60     60
##   [36,]     74     65     62     60     60     60     60     60     60
##   [37,]     89     75     67     62     60     60     60     60     60
##   [38,]     94     76     68     62     61     60     60     60     60
##   [39,]     81     60     65     60     60     60     60     60     60
##   [40,]     66     64     61     61     60     60     60     60     60
##   [41,]     65     64     60     60     60     60     60     60     60
##   [42,]     60     60     61     60     60     60     60     60     60
##   [43,]     82     60     60     60     60     60     60     60     60
##   [44,]    101     88     73     60     60     60     60     60     60
##   [45,]    121    113    110     80     68     60     64     60     60
##   [46,]    121    121     88     86     85     89     81     74     60
##   [47,]     99     72     85     93    112    113    112    109     84
##   [48,]     60     60     71     90    106    121    121    121    121
##   [49,]     61     61     64     72     90    100    109    110     80
##   [50,]     60     60     60     60     72     77     79     84     70
##   [51,]     60     60     60     60     60     60     60     66     66
##   [52,]     60     60     60     60     60     60     60     60     60
##   [53,]     60     60     60     60     60     60     60     60     60
##   [54,]     60     60     60     60     60     60     60     60     60
##   [55,]     60     60     60     60     60     60     60     60     60
##   [56,]     60     60     60     60     60     60     60     60     60
##   [57,]     60     60     60     60     60     60     60     60     60
##   [58,]     60     60     60     60     60     60     60     60     60
##   [59,]     60     60     60     60     60     60     60     60     60
##   [60,]     60     60     60     60     60     60     60     60     60
##   [61,]     60     60     60     60     60     60     60     60     60
##   [62,]     60     60     60     60     60     60     60     60     60
##   [63,]     60     60     60     60     60     60     60     60     60
##   [64,]     60     60     60     60     60     60     60     60     60
##   [65,]     60     60     60     60     60     60     60     60     60
##   [66,]     60     60     60     60     60     60     60     60     60
##   [67,]     60     60     60     60     60     60     60     60     60
##   [68,]     60     60     60     60     60     60     60     60     60
##   [69,]     60     60     60     60     60     60     60     60     60
##   [70,]     60     60     60     60     60     60     60     60     60
##   [71,]     60     60     60     60     60     60     60     60     60
##   [72,]     60     60     60     60     60     60     60     60     60
##   [73,]     71     60     60     60     60     60     60     60     60
##   [74,]     90     71     61     61     60     60     60     60     60
##   [75,]     90     70     61     61     60     60     60     60     60
##   [76,]     67     62     62     61     60     60     60     60     60
##   [77,]     60     60     61     61     60     60     60     60     60
##   [78,]     63     60     60     60     60     60     60     60     60
##   [79,]     60     61     60     60     60     60     60     60     60
##   [80,]     61     60     60     60     60     60     60     60     60
##   [81,]     60     60     60     60     60     60     60     60     60
##   [82,]     61     60     60     60     60     60     60     60     60
##   [83,]     60     60     60     60     60     60     60     60     60
##         [,560] [,561] [,562] [,563] [,564] [,565] [,566] [,567] [,568]
##    [1,]     28     28     28     28     29     30     31     32     33
##    [2,]     32     32     32     33     34     36     37     38     38
##    [3,]     37     37     37     37     39     41     42     43     43
##    [4,]     39     39     39     40     41     43     45     45     45
##    [5,]     41     41     41     42     44     45     46     46     47
##    [6,]     43     43     43     44     46     47     48     49     49
##    [7,]     45     45     46     46     48     49     50     51     52
##    [8,]     47     48     48     48     50     51     52     53     54
##    [9,]     50     50     50     51     52     53     54     55     56
##   [10,]     52     52     53     53     54     55     56     57     58
##   [11,]     53     54     54     55     56     56     57     58     59
##   [12,]     56     56     56     56     57     57     58     58     59
##   [13,]     58     58     58     58     58     59     59     59     60
##   [14,]     60     59     59     59     59     59     59     60     60
##   [15,]     69     60     60     60     60     60     60     60     60
##   [16,]     89     82     80     71     63     60     60     60     60
##   [17,]    109    100     98     91     78     67     60     60     60
##   [18,]    133    116    115    111     97     80     66     60     60
##   [19,]    182    152    151    182    121     96     82     71     60
##   [20,]    182    176    175    164    121    105     91     79     69
##   [21,]    168    182    174    148    134    117    103     91     79
##   [22,]    158    163    160    145    133    121    114    102     87
##   [23,]    140    145    140    131    128    125    122    115     98
##   [24,]    121    126    124    121    124    123    122    121    113
##   [25,]     79     91    107    118    121    122    122    122    121
##   [26,]     62     60     71    112    121    121    121    121    121
##   [27,]     60     60     60    115    119    121    121    121    121
##   [28,]     60     60     68     87    121    119    121    121    121
##   [29,]     60     60     60     70     75     91    111    121    100
##   [30,]     60     60     60     60     60     60     60     77     71
##   [31,]     60     60     60     60     60     60     60     60     63
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     60     60     60     60
##   [34,]     60     60     60     60     60     60     60     60     60
##   [35,]     60     60     60     60     60     60     60     60     60
##   [36,]     60     60     60     60     60     60     60     60     60
##   [37,]     60     60     60     60     60     60     60     60     60
##   [38,]     60     60     60     60     60     60     60     60     60
##   [39,]     60     60     60     60     60     60     60     60     60
##   [40,]     60     60     60     60     60     60     60     60     60
##   [41,]     60     60     60     60     60     60     60     60     60
##   [42,]     60     60     60     60     60     60     60     60     60
##   [43,]     60     60     60     60     60     60     60     60     60
##   [44,]     60     60     60     60     60     60     60     60     60
##   [45,]     60     60     60     60     60     60     60     60     60
##   [46,]     60     60     60     60     60     60     60     61     60
##   [47,]     60     60     60     60     60     60     60     66     60
##   [48,]     77     60     60     60     60     60     72     78     70
##   [49,]     73     64     60     60     60     79     88     97     89
##   [50,]     65     63     63     60     83     95    106    117    109
##   [51,]     63     62     65     83     97    121    121    120    121
##   [52,]     60     63     70     83     97    109    121    121    121
##   [53,]     60     64     74     81     92    105    121    121    117
##   [54,]     60     63     65     74     83     92    102    118    103
##   [55,]     60     60     60     60     71     77     82     86     81
##   [56,]     60     60     60     60     60     62     65     67     60
##   [57,]     60     60     60     60     60     60     60     61     61
##   [58,]     60     60     60     60     60     60     60     60     60
##   [59,]     60     60     60     60     60     60     60     60     60
##   [60,]     60     60     60     60     60     60     60     60     60
##   [61,]     60     60     60     60     60     60     60     60     60
##   [62,]     60     60     60     60     60     60     60     60     60
##   [63,]     60     60     60     60     60     60     60     60     60
##   [64,]     60     60     60     60     60     60     60     60     60
##   [65,]     60     60     60     60     60     60     60     60     59
##   [66,]     60     60     60     60     60     60     60     59     59
##   [67,]     60     60     60     60     60     60     60     59     59
##   [68,]     60     60     60     60     60     60     60     59     58
##   [69,]     60     60     60     60     60     60     60     59     58
##   [70,]     60     60     60     60     60     60     59     59     58
##   [71,]     60     60     60     60     60     60     59     58     57
##   [72,]     60     60     60     60     60     60     59     58     57
##   [73,]     60     60     60     60     60     60     59     58     56
##   [74,]     60     60     60     60     60     60     59     57     56
##   [75,]     60     60     60     60     60     60     59     57     56
##   [76,]     60     60     60     60     60     60     59     57     55
##   [77,]     60     60     60     60     60     60     58     56     55
##   [78,]     60     60     60     60     60     60     58     56     54
##   [79,]     60     60     60     60     60     60     58     56     54
##   [80,]     60     60     60     60     60     60     58     55     53
##   [81,]     60     60     60     60     60     60     58     55     53
##   [82,]     60     60     60     60     60     60     58     55     54
##   [83,]     60     60     60     60     60     60     58     55     54
##         [,569] [,570] [,571] [,572] [,573] [,574] [,575] [,576] [,577]
##    [1,]     34     35     36     38     40     42     45     51     59
##    [2,]     39     41     43     45     47     50     53     57     66
##    [3,]     44     46     48     50     53     56     59     63     74
##    [4,]     46     49     51     53     56     59     61     66     77
##    [5,]     48     51     52     55     57     60     63     70     81
##    [6,]     50     52     54     56     59     63     68     75     87
##    [7,]     53     54     56     59     64     69     76     83     93
##    [8,]     55     56     58     62     69     78     86     93    103
##    [9,]     57     58     61     64     74     88     97    104    115
##   [10,]     60     63     70     78     90    103    113    127    130
##   [11,]     64     75     84     95    108    113    131    155    170
##   [12,]     66     88    102    115    120    120    138    164    180
##   [13,]     66    106    121    119    121    121    134    154    165
##   [14,]     60     91    111    121    121    121    125    141    151
##   [15,]     60     60     60     60    121     91    110    126    136
##   [16,]     60     60     60     68     64     60     81    101    124
##   [17,]     60     60     60     60     60     60     60     60     92
##   [18,]     60     60     60     60     60     60     60     60     60
##   [19,]     60     60     60     60     60     60     60     60     60
##   [20,]     60     60     60     60     60     60     60     60     60
##   [21,]     64     60     60     60     60     60     60     60     60
##   [22,]     67     60     60     60     60     60     60     60     60
##   [23,]     75     60     60     60     60     59     59     59     59
##   [24,]     89     60     60     60     60     59     59     59     59
##   [25,]    109     80     65     60     60     59     58     58     58
##   [26,]    134     94     74     60     60     58     58     58     58
##   [27,]    146    100     74     63     59     58     58     58     58
##   [28,]    109     89     60     62     58     57     57     57     57
##   [29,]     81     66     61     59     57     57     57     57     57
##   [30,]     60     62     59     58     57     56     57     57     57
##   [31,]     61     60     59     56     57     56     56     56     56
##   [32,]     60     59     57     55     55     56     56     56     56
##   [33,]     60     58     56     54     54     54     55     55     55
##   [34,]     59     57     55     53     53     53     53     53     53
##   [35,]     59     56     54     51     51     51     51     51     51
##   [36,]     58     56     53     50     50     49     49     48     47
##   [37,]     58     55     51     48     48     47     46     44     42
##   [38,]     57     53     50     47     45     44     41     38     36
##   [39,]     56     53     49     45     41     37     33     30     27
##   [40,]     56     52     48     44     40     35     30     27     24
##   [41,]     56     52     48     44     41     35     30     26     23
##   [42,]     56     52     48     45     41     35     30     27     24
##   [43,]     56     52     49     45     42     37     32     29     26
##   [44,]     56     53     49     46     43     39     35     32     29
##   [45,]     57     53     50     47     45     41     38     35     32
##   [46,]     57     54     52     49     47     45     42     39     35
##   [47,]     58     56     54     52     51     49     46     42     39
##   [48,]     60     58     57     56     55     54     50     46     42
##   [49,]     78     67     60     60     60     59     54     49     45
##   [50,]     96     88     77     60     70     62     58     52     48
##   [51,]    115    113    110     92     79     67     60     53     49
##   [52,]    121    121    121    114     96     72     60     55     53
##   [53,]    121    121    121    121    109     71     60     57     56
##   [54,]     98    113    121    117    107     76     63     59     59
##   [55,]     60     82     97    104     86     72     67     67     64
##   [56,]     64     60     82     88     78     72     71     72     73
##   [57,]     60     60     73     76     73     74     75     79     83
##   [58,]     60     60     64     64     67     74     76     82     90
##   [59,]     60     60     60     60     60     60     60     71     81
##   [60,]     60     60     60     60     60     60     60     60     65
##   [61,]     60     60     59     59     59     60     60     60     60
##   [62,]     60     59     59     59     59     59     60     60     60
##   [63,]     59     59     58     58     59     58     58     59     59
##   [64,]     59     58     57     57     58     57     56     56     56
##   [65,]     58     58     57     57     57     56     55     54     53
##   [66,]     58     57     56     56     55     54     52     52     50
##   [67,]     58     57     55     55     54     52     50     49     47
##   [68,]     57     56     54     54     52     49     47     46     44
##   [69,]     57     56     53     53     50     47     45     43     41
##   [70,]     56     55     53     51     48     45     42     40     38
##   [71,]     56     55     52     49     46     42     40     38     35
##   [72,]     55     54     51     49     44     41     38     36     33
##   [73,]     55     53     51     48     44     40     38     35     32
##   [74,]     54     53     50     48     44     40     37     35     32
##   [75,]     54     53     50     47     43     39     37     35     32
##   [76,]     53     52     49     47     43     39     37     35     32
##   [77,]     53     51     49     45     42     40     37     35     33
##   [78,]     52     51     49     46     42     40     38     36     34
##   [79,]     52     50     49     46     43     41     39     37     35
##   [80,]     52     50     48     46     43     41     39     37     36
##   [81,]     52     50     48     46     43     41     39     38     36
##   [82,]     52     50     48     46     43     41     40     38     36
##   [83,]     52     50     49     46     43     42     40     38     36
##         [,578] [,579] [,580] [,581] [,582] [,583] [,584] [,585] [,586]
##    [1,]     69     81     94    108    123    136    147    157    162
##    [2,]     77     90    106    124    141    156    167    175    179
##    [3,]     86    101    120    141    162    179    186    192    195
##    [4,]     90    105    122    141    161    181    197    206    209
##    [5,]     94    109    125    144    166    189    207    217    218
##    [6,]    101    115    132    151    173    195    212    221    220
##    [7,]    105    119    136    157    179    200    214    219    215
##    [8,]    114    126    141    161    182    201    211    214    205
##    [9,]    124    134    146    160    176    197    219    215    198
##   [10,]    143    155    163    171    175    180    187    171    153
##   [11,]    166    169    174    178    165    161    157    153    138
##   [12,]    182    182    179    182    151    139    131    129    125
##   [13,]    176    182    182    182    131    120    113    110    102
##   [14,]    157    166    166    147    119    107    100     93     84
##   [15,]    140    145    141    133    114     95     85     77     69
##   [16,]    126    128    128    125    106     80     67     64     62
##   [17,]    121    122    122    121     91     60     64     61     60
##   [18,]     76    110    121    111     88     68     60     62     61
##   [19,]     72     83     87     92     76     60     63     61     61
##   [20,]     60     75     72     73     66     63     61     61     60
##   [21,]     60     60     63     62     61     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     59     59     60     59     59     59     59     59     59
##   [24,]     59     59     59     59     59     59     59     59     59
##   [25,]     58     59     59     59     59     59     59     59     59
##   [26,]     58     58     58     58     58     58     58     58     59
##   [27,]     58     58     58     58     58     58     58     58     59
##   [28,]     57     57     57     58     58     58     58     58     59
##   [29,]     57     57     57     57     58     58     58     58     59
##   [30,]     57     57     57     57     57     57     58     58     58
##   [31,]     56     56     56     57     57     57     57     57     57
##   [32,]     56     56     56     56     56     56     56     56     56
##   [33,]     55     55     54     54     54     54     54     54     54
##   [34,]     53     53     52     52     51     51     50     50     50
##   [35,]     50     50     49     48     46     46     45     44     44
##   [36,]     46     45     44     42     39     37     36     35     35
##   [37,]     41     39     37     34     29     27     25     25     26
##   [38,]     33     31     28     23     16     14     13     15     15
##   [39,]     24     21     17     10      0      0      0      5      6
##   [40,]     21     17     13      4      1      0      0      0      0
##   [41,]     19     16     12      6      2      0      0      0      0
##   [42,]     20     17     13      8      6      4      2      0      0
##   [43,]     23     19     16     12     10      8      6      3      1
##   [44,]     25     22     19     16     14     12     10      7      5
##   [45,]     29     26     23     19     17     16     14     12      9
##   [46,]     32     29     26     23     21     20     18     16     14
##   [47,]     35     32     30     27     25     24     23     21     18
##   [48,]     39     35     33     30     29     28     27     25     23
##   [49,]     41     39     37     34     33     33     32     30     28
##   [50,]     45     42     40     37     37     37     36     34     32
##   [51,]     47     45     42     40     40     40     39     37     35
##   [52,]     50     49     46     44     44     44     44     41     40
##   [53,]     53     52     50     48     48     49     48     46     45
##   [54,]     57     56     53     52     52     53     53     50     49
##   [55,]     60     60     57     56     56     57     57     54     54
##   [56,]     75     75     64     59     60     67     63     59     59
##   [57,]     89    101     91     60     97     88     76     68     62
##   [58,]     99    113    121    121    121    114     88     76     68
##   [59,]     88     93    112    121    121    103     96     81     70
##   [60,]     70     69     82    104     94     84     69     71     61
##   [61,]     60     60     60     69     69     60     60     60     57
##   [62,]     60     58     58     60     60     62     60     60     55
##   [63,]     56     55     55     56     54     55     57     57     47
##   [64,]     53     52     52     52     50     50     51     49     40
##   [65,]     50     49     48     48     45     44     45     42     34
##   [66,]     47     46     45     43     41     39     39     35     29
##   [67,]     44     42     41     39     36     33     32     29     23
##   [68,]     41     39     37     35     31     28     25     22     18
##   [69,]     38     35     33     30     27     24     21     18     14
##   [70,]     35     32     29     27     24     21     18     15     11
##   [71,]     33     29     26     23     21     18     16     14      9
##   [72,]     31     27     23     21     18     16     14     11      6
##   [73,]     30     26     22     20     17     15     12     10      6
##   [74,]     30     26     22     20     17     15     13     10      7
##   [75,]     30     26     23     20     18     16     14     11      8
##   [76,]     30     27     23     21     19     17     15     13     10
##   [77,]     31     28     24     22     21     18     17     15     12
##   [78,]     32     29     26     24     22     20     18     16     13
##   [79,]     33     30     28     25     24     22     20     17     14
##   [80,]     34     31     28     26     24     23     21     18     16
##   [81,]     34     32     29     27     25     24     22     19     17
##   [82,]     35     32     29     28     26     24     22     20     17
##   [83,]     35     33     30     28     26     25     23     21     18
##         [,587] [,588] [,589] [,590] [,591] [,592] [,593] [,594] [,595]
##    [1,]    165    167    170    174    180    187    195    204    213
##    [2,]    180    181    182    184    189    195    205    215    226
##    [3,]    195    194    194    194    198    205    216    228    241
##    [4,]    208    205    204    204    208    214    228    245    261
##    [5,]    216    213    212    213    217    223    238    254    269
##    [6,]    216    210    212    219    222    226    235    246    258
##    [7,]    207    200    205    214    214    217    221    229    239
##    [8,]    194    184    186    193    199    204    206    212    222
##    [9,]    175    165    168    174    178    189    189    193    199
##   [10,]    140    145    148    155    159    171    174    180    189
##   [11,]    128    125    127    137    143    154    162    171    183
##   [12,]    112    105    105    119    127    138    152    165    175
##   [13,]     92     85     86    110    118    121    145    162    176
##   [14,]     76     66     74    108    119    130    148    168    182
##   [15,]     60     64     81    121    131    146    164    182    195
##   [16,]     62     60    106    131    144    158    176    181    199
##   [17,]     61     60    106    136    150    164    182    182    191
##   [18,]     60     80    107    135    149    163    182    182    182
##   [19,]     60     75    109    130    142    151    160    167    165
##   [20,]     60     60     92    121    131    134    138    137    142
##   [21,]     60     60     69     77    103    106    106    106    121
##   [22,]     60     60     60     60     60     60     60     60     96
##   [23,]     59     60     60     60     60     60     60     60     77
##   [24,]     59     60     60     60     60     60     60     60     82
##   [25,]     59     59     60     60     60     60     60     60     75
##   [26,]     59     59     60     60     60     60     60     60     62
##   [27,]     59     59     60     60     60     60     60     60     60
##   [28,]     59     59     60     60     60     60     60     60     60
##   [29,]     59     59     60     60     60     60     60     60     60
##   [30,]     58     59     60     60     60     60     60     60     59
##   [31,]     57     58     59     60     60     60     60     60     59
##   [32,]     56     56     57     58     60     60     60     60     58
##   [33,]     54     54     56     56     58     60     60     60     53
##   [34,]     50     51     52     53     54     58     60     60     51
##   [35,]     44     44     45     46     47     50     55     55     47
##   [36,]     35     36     37     38     39     42     46     43     37
##   [37,]     26     27     28     29     30     32     35     32     27
##   [38,]     16     18     19     20     21     23     25     22     21
##   [39,]      6      9     10     11     12     13     14     13     13
##   [40,]      0      3      4      5      6      7      7      7      6
##   [41,]      0      0      0      1      1      1      1      1      1
##   [42,]      0      0      0      0      0      0      0      0      0
##   [43,]      0      0      0      0      0      0      0      0      0
##   [44,]      1      0      0      0      2      2      2      1      2
##   [45,]      5      2      2      5      5      5      5      4      4
##   [46,]     10      7      8      9      9      9      8      7      7
##   [47,]     14     12     12     13     13     12     11     10      9
##   [48,]     19     17     17     17     17     16     14     12     11
##   [49,]     24     21     21     21     19     18     17     14     12
##   [50,]     29     26     26     25     23     21     19     17     14
##   [51,]     32     29     29     28     26     24     22     19     16
##   [52,]     36     34     33     32     30     28     24     21     19
##   [53,]     41     39     38     35     33     31     27     24     21
##   [54,]     46     43     42     39     37     34     30     26     24
##   [55,]     51     48     46     43     40     37     33     29     26
##   [56,]     55     53     50     47     44     40     36     31     28
##   [57,]     60     57     56     51     47     43     38     33     30
##   [58,]     62     60     58     53     49     45     39     34     31
##   [59,]     62     56     54     50     48     44     39     34     31
##   [60,]     56     53     50     48     45     42     38     33     31
##   [61,]     51     47     45     43     40     38     35     31     29
##   [62,]     46     42     40     38     36     34     31     28     26
##   [63,]     40     36     34     33     31     29     26     24     22
##   [64,]     34     30     29     27     25     23     21     18     17
##   [65,]     29     25     23     21     18     17     15     13     12
##   [66,]     23     19     17     14     11     10      9      8      7
##   [67,]     17     14     10      7      3      4      4      4      4
##   [68,]     12      9      5      0      1      0      1      1      1
##   [69,]      9      6      3      0      0      0      0      0      0
##   [70,]      6      3      1      0      0      0      0      0      0
##   [71,]      4      2      1      0      0      0      0      0      0
##   [72,]      1      0      0      0      0      0      0      0      0
##   [73,]      3      2      1      0      0      0      0      0      0
##   [74,]      4      3      2      2      1      0      0      0      0
##   [75,]      6      5      4      3      2      1      0      0      0
##   [76,]      7      6      5      4      3      2      1      0      0
##   [77,]      9      8      7      5      4      2      1      0      0
##   [78,]     11      9      8      6      5      3      1      0      0
##   [79,]     13     11     10      8      6      4      2      1      0
##   [80,]     14     12     11      9      7      5      3      1      0
##   [81,]     15     13     12     10      8      6      3      2      1
##   [82,]     16     14     12     10      9      7      4      3      1
##   [83,]     16     15     13     11     10      8      5      3      2
##         [,596] [,597] [,598] [,599] [,600] [,601] [,602] [,603] [,604]
##    [1,]    218    214    208    200    189    175    162    147    135
##    [2,]    234    232    227    219    206    190    174    156    145
##    [3,]    251    250    246    236    220    200    178    156    147
##    [4,]    265    264    261    254    241    224    205    188    180
##    [5,]    273    274    271    266    258    246    233    218    207
##    [6,]    269    271    274    273    268    260    254    242    230
##    [7,]    250    260    266    271    273    272    267    257    246
##    [8,]    233    245    256    266    276    283    278    268    257
##    [9,]    217    231    246    261    282    294    296    270    257
##   [10,]    211    227    242    258    276    288    286    279    262
##   [11,]    202    218    231    244    259    271    266    256    230
##   [12,]    191    215    228    237    243    251    252    243    208
##   [13,]    190    212    226    237    240    243    243    219    182
##   [14,]    200    219    232    242    242    242    243    236    212
##   [15,]    215    232    243    240    243    243    243    243    243
##   [16,]    217    235    242    243    243    243    243    243    243
##   [17,]    206    215    218    234    243    243    243    243    243
##   [18,]    194    202    201    216    233    243    243    243    243
##   [19,]    177    184    182    192    216    243    243    243    233
##   [20,]    159    165    174    179    182    217    243    243    224
##   [21,]    140    151    161    170    178    190    222    243    217
##   [22,]    121    137    149    157    164    172    192    198    202
##   [23,]    121    129    138    144    149    154    166    171    167
##   [24,]    101    121    128    131    133    135    140    136    134
##   [25,]     87     95     98     91    101     91    111    106    108
##   [26,]     66     68     60     64     60     63     60     60     75
##   [27,]     60     61     58     57     57     58     59     60     60
##   [28,]     59     57     54     53     52     52     55     58     60
##   [29,]     58     56     52     50     47     47     49     51     52
##   [30,]     56     53     48     46     42     41     41     42     43
##   [31,]     53     49     44     41     37     35     33     33     33
##   [32,]     51     46     40     36     32     28     25     24     23
##   [33,]     47     42     36     32     27     22     16     14     13
##   [34,]     44     38     32     27     22     15      8      3      3
##   [35,]     40     34     28     22     17      9      0      1      0
##   [36,]     32     28     23     18     13      6      0      0      0
##   [37,]     24     20     16     12      8      1      0      0      0
##   [38,]     18     15     11      8      4      0      0      0      0
##   [39,]     11      8      5      1      0      0      0      0      0
##   [40,]      5      3      0      1      0      0      0      0      0
##   [41,]      1      0      0      0      0      0      0      0      0
##   [42,]      0      0      0      0      0      0      0      0      0
##   [43,]      0      0      1      1      1      0      0      0      0
##   [44,]      2      2      2      2      1      0      0      0      0
##   [45,]      4      4      3      3      2      1      0      0      0
##   [46,]      6      5      4      3      3      1      1      0      0
##   [47,]      8      7      5      5      3      2      1      0      0
##   [48,]      9      8      7      6      4      3      1      0      0
##   [49,]     10      9      8      7      5      3      2      1      0
##   [50,]     12     11      9      8      5      3      2      1      0
##   [51,]     14     13     11      9      6      4      2      1      0
##   [52,]     16     14     12     10      7      4      3      1      0
##   [53,]     19     17     14     12      9      5      3      1      0
##   [54,]     21     19     16     14     10      7      5      2      1
##   [55,]     23     21     18     15     11      8      6      3      1
##   [56,]     25     22     19     17     13      9      7      4      2
##   [57,]     27     24     21     18     14     10      8      5      3
##   [58,]     28     25     22     19     15     11      9      7      4
##   [59,]     28     25     23     20     16     12     10      7      5
##   [60,]     28     25     22     20     16     12     10      8      6
##   [61,]     26     24     21     18     15     12     10      8      6
##   [62,]     24     21     20     17     14     12     10      8      7
##   [63,]     20     18     17     14     12     10      9      7      6
##   [64,]     16     14     13     11      9      8      7      6      4
##   [65,]     11     10      9      8      6      5      5      4      3
##   [66,]      7      6      6      5      4      3      3      2      1
##   [67,]      3      3      3      2      2      1      1      1      0
##   [68,]      1      1      1      1      0      0      0      0      0
##   [69,]      0      0      0      0      0      0      0      0      0
##   [70,]      0      0      0      0      0      0      0      0      0
##   [71,]      0      0      0      0      0      0      0      0      0
##   [72,]      0      0      0      0      0      0      0      0      0
##   [73,]      0      0      0      0      0      0      0      0      0
##   [74,]      0      0      0      0      0      0      0      0      0
##   [75,]      0      0      0      0      0      0      0      0      0
##   [76,]      0      0      0      0      0      0      0      0      0
##   [77,]      0      0      0      0      0      0      0      0      0
##   [78,]      0      0      0      0      0      0      0      0      0
##   [79,]      0      0      0      0      0      0      0      0      0
##   [80,]      0      0      0      0      0      0      0      0      0
##   [81,]      0      0      0      0      0      0      0      0      0
##   [82,]      0      0      0      0      0      0      0      0      0
##   [83,]      1      0      0      0      0      0      0      0      0
##         [,605] [,606] [,607] [,608] [,609] [,610] [,611] [,612] [,613]
##    [1,]    127    126    129    128    121    112    101     90     80
##    [2,]    138    145    150    145    136    124    111     97     86
##    [3,]    153    165    169    161    149    132    113     98     85
##    [4,]    174    183    185    178    167    153    139    125    112
##    [5,]    201    201    200    192    184    172    159    146    134
##    [6,]    222    217    211    202    193    182    171    161    152
##    [7,]    238    228    219    208    196    184    173    164    158
##    [8,]    246    236    220    204    188    173    161    153    153
##    [9,]    243    228    211    192    171    153    138    129    137
##   [10,]    238    214    194    172    151    132    120    108    114
##   [11,]    207    188    170    150    130    111     96     86     88
##   [12,]    182    166    145    129    113     90     68     62     61
##   [13,]    178    154    121    125    105     82     60     60     61
##   [14,]    182    165    152    135    112     90     77     65     60
##   [15,]    207    182    178    182    152    101     86     73     63
##   [16,]    222    199    182    177    138    109     92     77     60
##   [17,]    237    211    198    182    143    118    103     89     78
##   [18,]    227    220    202    186    162    121    114    102     91
##   [19,]    220    206    194    186    183    169    137    116    106
##   [20,]    209    193    182    184    182    183    182    140    121
##   [21,]    197    182    172    167    170    171    153    140    126
##   [22,]    182    157    145    142    149    147    138    130    126
##   [23,]    152    131    119    122    128    128    129    126    123
##   [24,]    121    111    103     98     81     60    121    121    121
##   [25,]     99     92     85     71     63     63     60     85     85
##   [26,]     78     76     71     61     58     58     58     60     64
##   [27,]     67     68     66     60     56     53     55     57     60
##   [28,]     60     61     62     58     50     47     48     51     50
##   [29,]     57     60     60     48     42     41     42     44     42
##   [30,]     46     48     47     40     35     34     35     37     35
##   [31,]     36     38     37     32     28     28     28     30     28
##   [32,]     25     28     27     25     22     22     22     23     21
##   [33,]     14     18     18     18     16     15     15     15     14
##   [34,]      3      9      9     11     10     10      9      9      8
##   [35,]      0      0      2      4      5      5      5      4      4
##   [36,]      0      0      0      0      1      1      1      1      1
##   [37,]      0      0      0      0      0      0      0      0      0
##   [38,]      0      0      0      0      0      0      0      0      0
##   [39,]      0      0      0      0      0      0      0      0      0
##   [40,]      0      0      0      0      0      0      0      0      0
##   [41,]      0      0      0      0      0      0      0      0      0
##   [42,]      0      0      0      0      0      0      0      0      0
##   [43,]      0      0      0      0      0      0      0      0      0
##   [44,]      0      0      0      0      0      0      0      0      0
##   [45,]      0      0      0      0      0      0      0      0      0
##   [46,]      0      0      0      0      0      0      0      0      0
##   [47,]      0      0      0      0      0      0      0      0      0
##   [48,]      0      0      0      0      0      0      0      0      0
##   [49,]      0      0      0      0      0      0      0      0      0
##   [50,]      0      0      0      0      0      0      0      0      0
##   [51,]      0      0      0      0      0      0      0      0      0
##   [52,]      0      0      0      0      0      0      0      0      0
##   [53,]      0      0      0      0      0      0      0      0      0
##   [54,]      0      0      0      0      0      0      0      0      0
##   [55,]      0      0      0      0      0      0      0      0      0
##   [56,]      0      0      0      0      0      0      0      0      0
##   [57,]      1      0      0      0      0      0      0      0      0
##   [58,]      2      0      0      0      0      0      0      0      0
##   [59,]      3      0      0      0      0      0      0      0      0
##   [60,]      4      1      0      0      0      0      0      0      0
##   [61,]      5      2      0      0      0      0      0      0      0
##   [62,]      5      3      1      0      0      0      0      0      0
##   [63,]      5      3      1      0      0      0      0      0      0
##   [64,]      3      2      1      0      0      0      0      0      0
##   [65,]      2      1      0      0      0      0      0      0      0
##   [66,]      1      0      0      0      0      0      0      0      0
##   [67,]      0      0      0      0      0      0      0      0      0
##   [68,]      0      0      0      0      0      0      0      0      0
##   [69,]      0      0      0      0      0      0      0      0      0
##   [70,]      0      0      0      0      0      0      0      0      0
##   [71,]      0      0      0      0      0      0      0      0      0
##   [72,]      0      0      0      0      0      0      0      0      0
##   [73,]      0      0      0      0      0      0      0      0      0
##   [74,]      0      0      0      0      0      0      0      0      0
##   [75,]      0      0      0      0      0      0      0      0      0
##   [76,]      0      0      0      0      0      0      0      0      0
##   [77,]      0      0      0      0      0      0      0      0      0
##   [78,]      0      0      0      0      0      0      0      0      0
##   [79,]      0      0      0      0      0      0      0      0      0
##   [80,]      0      0      0      0      0      0      0      0      0
##   [81,]      0      0      0      0      0      0      0      0      0
##   [82,]      0      0      0      0      0      0      0      0      0
##   [83,]      0      0      0      0      0      0      0      0      0
##         [,614] [,615] [,616] [,617] [,618] [,619] [,620] [,621] [,622]
##    [1,]     72     64     60     60     62     65     71     79     88
##    [2,]     77     72     70     69     71     73     79     88     98
##    [3,]     84     83     82     81     82     83     88    100    112
##    [4,]    102    101    101     99     98     97    100    106    114
##    [5,]    125    123    124    122    118    113    114    113    114
##    [6,]    146    144    145    145    138    130    128    120    112
##    [7,]    163    165    167    163    155    148    140    122    105
##    [8,]    161    166    170    173    167    157    138    114     94
##    [9,]    148    162    171    177    168    157    140    110     84
##   [10,]    130    146    160    168    154    142    131    111     87
##   [11,]    108    124    137    143    133    124    119    105     87
##   [12,]     60     92    124    126    121    109    105    102     82
##   [13,]     60     60     91    121     97     89     74     60     60
##   [14,]     60     60     60     70     72     67     62     62     61
##   [15,]     60     60     60     60     60     60     60     61     60
##   [16,]     61     60     60     60     60     60     60     60     60
##   [17,]     66     60     60     60     60     60     60     60     60
##   [18,]     80     65     60     60     60     60     60     60     60
##   [19,]     93     80     67     63     60     60     60     60     60
##   [20,]    106     95     83     74     65     60     60     60     60
##   [21,]    118    111     95     82     71     63     60     60     59
##   [22,]    124    121    108     87     71     60     61     60     56
##   [23,]    122    122    107     86     65     61     60     60     56
##   [24,]    106     91     81     68     69     60     60     60     56
##   [25,]     80     64     59     60     62     63     60     60     57
##   [26,]     60     55     55     56     59     60     61     60     59
##   [27,]     55     50     51     53     54     57     60     60     60
##   [28,]     46     42     45     48     50     52     57     60     60
##   [29,]     39     35     38     40     42     43     47     49     55
##   [30,]     32     29     31     32     32     33     35     35     38
##   [31,]     25     22     22     22     22     21     21     20     20
##   [32,]     18     16     15     13     12     11      9      6      3
##   [33,]     13     11      9      8      6      4      2      0      0
##   [34,]      8      6      5      4      3      1      0      0      0
##   [35,]      3      3      3      2      1      0      0      0      0
##   [36,]      1      1      1      1      0      0      0      0      0
##   [37,]      0      0      0      0      0      0      0      0      0
##   [38,]      0      0      0      0      0      0      0      0      0
##   [39,]      0      0      0      0      0      0      0      0      0
##   [40,]      0      0      0      0      0      0      0      0      0
##   [41,]      0      0      0      0      0      0      0      0      0
##   [42,]      0      0      0      0      0      0      0      0      0
##   [43,]      0      0      0      0      0      0      0      0      0
##   [44,]      0      0      0      0      0      0      0      0      0
##   [45,]      0      0      0      0      0      0      0      0      0
##   [46,]      0      0      0      0      0      0      0      0      0
##   [47,]      0      0      0      0      0      0      0      0      0
##   [48,]      0      0      0      0      0      0      0      0      0
##   [49,]      0      0      0      0      0      0      0      0      0
##   [50,]      0      0      0      0      0      0      0      0      0
##   [51,]      0      0      0      0      0      0      0      0      0
##   [52,]      0      0      0      0      0      0      0      0      0
##   [53,]      0      0      0      0      0      0      0      0      0
##   [54,]      0      0      0      0      0      0      0      0      0
##   [55,]      0      0      0      0      0      0      0      0      0
##   [56,]      0      0      0      0      0      0      0      0      0
##   [57,]      0      0      0      0      0      0      0      0      0
##   [58,]      0      0      0      0      0      0      0      0      0
##   [59,]      0      0      0      0      0      0      0      0      0
##   [60,]      0      0      0      0      0      0      0      0      0
##   [61,]      0      0      0      0      0      0      0      0      0
##   [62,]      0      0      0      0      0      0      0      0      0
##   [63,]      0      0      0      0      0      0      0      0      0
##   [64,]      0      0      0      0      0      0      0      0      0
##   [65,]      0      0      0      0      0      0      0      0      0
##   [66,]      0      0      0      0      0      0      0      0      0
##   [67,]      0      0      0      0      0      0      0      0      0
##   [68,]      0      0      0      0      0      0      0      0      0
##   [69,]      0      0      0      0      0      0      0      0      0
##   [70,]      0      0      0      0      0      0      0      0      0
##   [71,]      0      0      0      0      0      0      0      0      0
##   [72,]      0      0      0      0      0      0      0      0      0
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##         [,623] [,624] [,625] [,626] [,627] [,628] [,629] [,630] [,631]
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##    [2,]    107    114    114    111    107     99     90     81     73
##    [3,]    121    121    120    114    106     98     87     78     70
##    [4,]    118    117    109    103     95     86     79     72     66
##    [5,]    113    109    101     93     85     78     72     68     63
##    [6,]    105     97     90     82     76     71     68     65     62
##    [7,]     94     86     80     74     69     66     64     63     60
##    [8,]     81     74     70     67     64     63     62     62     58
##    [9,]     71     64     62     62     61     61     62     61     57
##   [10,]     72     64     61     60     60     60     61     60     55
##   [11,]     73     64     61     60     60     60     61     60     53
##   [12,]     60     62     61     60     60     60     61     62     50
##   [13,]     65     61     60     60     60     60     62     62     48
##   [14,]     60     62     60     60     60     60     61     61     46
##   [15,]     60     60     60     60     60     60     60     61     43
##   [16,]     60     60     59     58     58     60     60     46     40
##   [17,]     60     59     58     56     56     56     54     43     37
##   [18,]     60     58     56     54     53     53     50     40     35
##   [19,]     59     57     55     52     50     49     45     37     32
##   [20,]     58     55     52     49     47     44     40     35     30
##   [21,]     56     53     50     46     44     40     35     32     28
##   [22,]     54     50     47     44     41     36     30     27     23
##   [23,]     52     49     45     42     38     32     26     22     18
##   [24,]     52     48     45     41     37     31     24     19     14
##   [25,]     53     49     46     42     38     31     23     18     13
##   [26,]     55     53     50     46     42     33     23     16     10
##   [27,]     60     60     60     53     49     37     23     15      7
##   [28,]     60     60     60     60     60     46     25     14      5
##   [29,]     60     60     60     60     51     39     23     11      0
##   [30,]     39     38     41     37     33     24     17      9      0
##   [31,]     19     15     22     21     18     14      9      5      2
##   [32,]      3      1      5      5      5      6      2      1      0
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##   [83,]      0      0      0      0      0      0      0      0      0
##         [,632] [,633] [,634] [,635] [,636] [,637] [,638] [,639] [,640]
##    [1,]     66     61     57     53     50     47     43     40     36
##    [2,]     66     60     55     50     45     42     39     36     33
##    [3,]     63     56     50     45     41     37     35     33     30
##    [4,]     60     54     48     43     39     35     33     31     29
##    [5,]     58     52     46     41     37     34     32     31     28
##    [6,]     56     50     45     40     36     33     31     31     28
##    [7,]     54     49     43     38     35     32     31     31     28
##    [8,]     52     47     42     37     34     32     31     30     28
##    [9,]     50     45     40     36     33     31     30     30     28
##   [10,]     48     43     39     35     33     31     30     30     28
##   [11,]     46     42     38     34     32     30     30     30     28
##   [12,]     44     40     37     32     31     30     30     30     29
##   [13,]     42     39     35     31     31     29     29     30     29
##   [14,]     41     38     35     30     30     29     29     30     29
##   [15,]     39     36     33     30     30     29     29     30     30
##   [16,]     37     35     32     29     29     29     29     30     30
##   [17,]     35     33     31     28     28     29     29     29     30
##   [18,]     34     32     30     27     27     28     28     27     27
##   [19,]     32     31     29     26     24     24     23     22     21
##   [20,]     28     27     25     22     19     17     15     11     11
##   [21,]     23     20     17     13      8      6      2      0      0
##   [22,]     19     15      9      3      0      0      0      0      0
##   [23,]     14      9      3      0      0      0      0      0      0
##   [24,]      9      5      0      0      0      0      0      0      0
##   [25,]      7      3      0      0      0      0      0      0      0
##   [26,]      4      0      0      0      0      0      0      0      0
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##   [83,]      0      0      0      0      0      0      0      0      0
##         [,641] [,642] [,643] [,644] [,645] [,646] [,647] [,648] [,649]
##    [1,]     32     28     24     20     16     13      9      6      4
##    [2,]     29     25     22     19     15     12      9      6      4
##    [3,]     26     23     20     17     14     11      9      6      4
##    [4,]     26     23     20     17     15     12     10      8      5
##    [5,]     26     23     21     18     17     14     12     11      7
##    [6,]     27     24     22     19     18     16     14     13      9
##    [7,]     27     24     23     21     20     18     17     15     12
##    [8,]     27     25     24     22     22     20     19     17     14
##    [9,]     28     26     25     24     24     22     21     19     16
##   [10,]     28     26     26     25     25     24     24     22     19
##   [11,]     28     27     28     27     28     27     27     24     21
##   [12,]     29     28     28     28     29     28     29     26     24
##   [13,]     29     29     30     30     31     31     31     29     28
##   [14,]     30     30     31     32     33     33     34     34     33
##   [15,]     30     31     32     34     35     36     37     38     40
##   [16,]     31     32     33     34     35     36     38     40     42
##   [17,]     30     32     32     33     34     36     38     41     44
##   [18,]     28     28     29     30     32     34     36     39     44
##   [19,]     21     22     22     24     27     30     33     37     43
##   [20,]     10     10     11     15     20     24     28     34     41
##   [21,]      0      0      0      4     10     16     21     29     38
##   [22,]      0      0      0      0      0      7     10     21     33
##   [23,]      0      0      0      0      0      0      0     13     25
##   [24,]      0      0      0      0      0      0      0      2     13
##   [25,]      0      0      0      0      0      0      0      0      0
##   [26,]      0      0      0      0      0      0      0      0      0
##   [27,]      0      0      0      0      0      0      0      0      0
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##   [30,]      0      0      0      0      0      0      0      0      0
##   [31,]      0      0      0      0      0      0      0      0      0
##   [32,]      0      0      0      0      0      0      0      0      0
##   [33,]      0      0      0      0      0      0      0      0      0
##   [34,]      0      0      0      0      0      0      0      0      0
##   [35,]      0      0      0      0      0      0      0      0      0
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##   [82,]      0      0      0      0      0      0      0      0      0
##   [83,]      0      0      0      0      0      0      0      0      0
##         [,650] [,651] [,652] [,653] [,654] [,655] [,656] [,657] [,658]
##    [1,]      2      1      1      0      0      0      0      0      0
##    [2,]      2      1      0      0      0      0      0      0      0
##    [3,]      2      1      0      0      0      0      0      0      0
##    [4,]      3      1      0      0      0      0      0      0      0
##    [5,]      5      3      1      0      0      0      0      0      0
##    [6,]      7      5      3      1      0      0      0      0      0
##    [7,]      9      7      5      3      1      0      0      0      0
##    [8,]     12      9      8      6      4      1      0      0      0
##    [9,]     14     12     10      8      6      3      1      0      0
##   [10,]     17     15     13     11     10      7      4      2      1
##   [11,]     20     18     17     15     14     11      9      6      3
##   [12,]     22     21     19     18     17     15     12     10      8
##   [13,]     27     26     25     24     24     23     22     22     24
##   [14,]     33     33     33     33     34     35     36     38     45
##   [15,]     40     41     42     43     45     47     50     53     60
##   [16,]     44     46     48     49     51     54     57     60     59
##   [17,]     46     48     51     53     57     58     60     60     60
##   [18,]     46     50     53     56     59     60     60     60     55
##   [19,]     47     51     55     59     60     60     56     50     46
##   [20,]     46     51     56     59     60     60     50     42     35
##   [21,]     44     51     59     60     60     60     45     35     27
##   [22,]     40     48     60     60     55     40     33     23     14
##   [23,]     33     40     48     60     39     25     18      8      0
##   [24,]     19     24     30     27     19      7      4      0      0
##   [25,]      3      7      9     10      3      2      0      0      0
##   [26,]      0      0      1      1      0      0      0      0      0
##   [27,]      0      0      0      0      0      0      0      0      0
##   [28,]      0      0      0      0      0      0      0      0      0
##   [29,]      0      0      0      0      0      0      0      0      0
##   [30,]      0      0      0      0      0      0      0      0      0
##   [31,]      0      0      0      0      0      0      0      0      0
##   [32,]      0      0      0      0      0      0      0      0      0
##   [33,]      0      0      0      0      0      0      0      0      0
##   [34,]      0      0      0      0      0      0      0      0      0
##   [35,]      0      0      0      0      0      0      0      0      0
##   [36,]      0      0      0      0      0      0      0      0      0
##   [37,]      0      0      0      0      0      0      0      0      0
##   [38,]      0      0      0      0      0      0      0      0      0
##   [39,]      0      0      0      0      0      0      0      0      0
##   [40,]      0      0      0      0      0      0      0      0      0
##   [41,]      0      0      0      0      0      0      0      0      0
##   [42,]      0      0      0      0      0      0      0      0      0
##   [43,]      0      0      0      0      0      0      0      0      0
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##   [48,]     48     35     28     23     12      9      9      8      8
##   [49,]     55     49     44     33     18     16     16     14     14
##   [50,]     57     60     60     40     23     24     22     21     18
##   [51,]     48     56     60     39     28     31     29     27     23
##   [52,]     38     46     49     33     34     38     35     33     30
##   [53,]     28     37     41     36     40     46     46     45     40
##   [54,]     19     28     34     42     48     54     60     60     52
##   [55,]     11     19     26     38     49     57     60     60     60
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##   [49,]     11      7      3      0      0      0      0      0      0
##   [50,]     15     11      6      3      0      0      0      0      0
##   [51,]     20     15      9      5      1      0      0      0      0
##   [52,]     26     19     13      7      0      0      0      0      0
##   [53,]     35     28     21     16     10      3      0      0      0
##   [54,]     46     38     30     27     21     14     10      1      0
##   [55,]     57     48     40     39     33     26     21     12      5
##   [56,]     60     57     51     52     45     37     32     23     17
##   [57,]     60     60     59     60     53     45     39     30     24
##   [58,]     59     60     65     65     64     56     50     40     35
##   [59,]     56     60     68     75     78     74     60     50     46
##   [60,]     54     60     74     88    100    108     80     59     57
##   [61,]     56     68     78     99    121    121    106     75     60
##   [62,]     51     59     68     96    121    121    120    118     81
##   [63,]     49     58     60     86    121    112    115    121    121
##   [64,]     48     60     65     70     69     86     95    109    121
##   [65,]     43     53     60     60     60     60     73     85     98
##   [66,]     36     45     49     49     52     56     59     66     82
##   [67,]     27     36     41     42     46     49     55     60     68
##   [68,]     21     30     35     38     42     46     51     57     60
##   [69,]     12     21     28     32     36     40     47     53     57
##   [70,]      3     11     21     25     30     35     42     49     53
##   [71,]      0      2     14     19     24     29     37     44     49
##   [72,]      0      0      7     13     19     24     32     40     45
##   [73,]      0      0      3      9     15     21     30     38     44
##   [74,]      0      0      0      8     14     21     30     38     44
##   [75,]      0      0      6     10     16     23     32     41     48
##   [76,]      0      0      7     14     20     26     35     46     53
##   [77,]      0      1      8     14     21     28     38     49     55
##   [78,]      0      3      9     15     22     29     41     54     60
##   [79,]      0      3      8     15     22     30     42     60     59
##   [80,]      0      0      2     11     18     26     36     47     53
##   [81,]      0      0      0      4     11     18     27     35     37
##   [82,]      0      0      0      0      2     11     17     21     23
##   [83,]      0      0      0      0      0      1      5      7      8
##         [,713] [,714] [,715] [,716] [,717] [,718] [,719] [,720] [,721]
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##    [3,]      0      0      0      0      0      0      0      0      0
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##    [5,]      0      0      0      0      0      0      0      0      0
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##   [55,]      3      1      0      0      0      0      0      0      0
##   [56,]     14      9      6      2      0      0      0      0      0
##   [57,]     20     15     12      8      6      1      0      0      0
##   [58,]     28     23     19     15     12      8      4      2      1
##   [59,]     37     30     27     22     17     13     10      9      6
##   [60,]     44     38     34     29     24     19     16     15     12
##   [61,]     51     45     41     35     30     25     22     21     18
##   [62,]     58     53     48     42     36     31     28     26     24
##   [63,]     94     60     56     48     42     37     34     32     31
##   [64,]    109     82     60     54     48     43     39     38     37
##   [65,]     89     73     70     60     54     49     45     44     43
##   [66,]     73     66     64     65     61     55     51     48     47
##   [67,]     65     62     61     66     70     60     56     54     54
##   [68,]     62     61     61     70     79     71     60     60     60
##   [69,]     60     60     60     77     97     91     93     88     87
##   [70,]     57     60     60     86    118    115    121    113    113
##   [71,]     53     57     60     68    110    121    120    121    121
##   [72,]     50     54     58     60    107    121    121    121    121
##   [73,]     49     53     57     60    109    121    121    121    112
##   [74,]     49     54     58     60    117    120    121    121    106
##   [75,]     54     59     71    109    121    120    121    110     94
##   [76,]     60     71     86    121    121    107     99     91     73
##   [77,]     59     60     69     81     85     93     84     76     60
##   [78,]     60     60     60     61     60     67     69     66     65
##   [79,]     60     60     60     60     61     60     60     62     62
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##         [,740] [,741] [,742] [,743] [,744] [,745] [,746] [,747] [,748]
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##         [,749] [,750] [,751] [,752] [,753] [,754] [,755] [,756] [,757]
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##   [82,]      0      0      0      0      0      0      0      0      0
##   [83,]      0      0      0      0      0      0      0      0      0
##         [,758] [,759] [,760] [,761] [,762] [,763] [,764] [,765] [,766]
##    [1,]      0      0      1      1      3      6      9     13     17
##    [2,]      0      0      0      2      4      7     10     13     16
##    [3,]      0      0      0      1      4      7     10     13     15
##    [4,]      0      0      0      0      2      4      7     10     11
##    [5,]      0      0      0      0      0      1      3      6      7
##    [6,]      0      0      0      0      0      0      1      2      3
##    [7,]      0      0      0      0      0      0      0      0      1
##    [8,]      0      0      0      0      0      0      0      0      0
##    [9,]      0      0      0      0      0      0      0      0      0
##   [10,]      0      0      0      0      0      0      0      0      0
##   [11,]      0      0      0      0      0      0      0      0      0
##   [12,]      0      0      0      0      0      0      0      0      0
##   [13,]      0      0      0      0      0      0      0      0      0
##   [14,]      0      0      0      0      0      0      0      0      0
##   [15,]      0      0      0      0      0      0      0      0      0
##   [16,]      0      0      0      0      0      0      0      0      0
##   [17,]      0      0      0      0      0      0      0      0      0
##   [18,]      0      0      0      0      0      0      0      0      0
##   [19,]      0      0      0      0      0      0      0      0      0
##   [20,]      0      0      0      0      0      0      0      0      0
##   [21,]      0      0      0      0      0      0      0      0      0
##   [22,]      0      0      0      0      0      0      0      0      0
##   [23,]      0      0      0      0      0      0      0      0      0
##   [24,]      0      0      0      0      0      0      0      0      0
##   [25,]      0      0      0      0      0      0      0      0      0
##   [26,]      0      0      0      0      0      0      0      0      0
##   [27,]      0      0      0      0      0      0      0      0      0
##   [28,]      0      0      0      0      0      0      0      0      0
##   [29,]      0      0      0      0      0      0      0      0      0
##   [30,]      0      0      0      0      0      0      0      0      0
##   [31,]      0      0      0      0      0      0      0      0      0
##   [32,]      0      0      0      0      0      0      0      0      0
##   [33,]      0      0      0      0      0      0      0      0      0
##   [34,]      0      0      0      0      0      0      0      0      0
##   [35,]      0      0      0      0      0      0      0      0      0
##   [36,]      0      0      0      0      0      0      0      0      0
##   [37,]      0      0      0      0      0      0      0      0      0
##   [38,]      0      0      0      0      0      0      0      0      0
##   [39,]      0      0      0      0      0      0      0      0      0
##   [40,]      0      0      0      0      0      0      0      0      0
##   [41,]      0      0      0      0      0      0      0      0      0
##   [42,]      0      0      0      0      0      0      0      0      0
##   [43,]      0      0      0      0      0      0      0      0      0
##   [44,]      0      0      0      0      0      0      0      0      0
##   [45,]      0      0      0      0      0      0      0      0      0
##   [46,]      0      0      0      0      0      0      0      0      0
##   [47,]      0      0      0      0      0      0      0      0      0
##   [48,]      0      0      0      0      0      0      0      0      0
##   [49,]      0      0      0      0      0      0      0      0      0
##   [50,]      0      0      0      0      0      0      0      0      0
##   [51,]      0      0      0      0      0      0      0      0      0
##   [52,]      0      0      0      0      0      0      0      0      0
##   [53,]      0      0      0      0      0      0      0      0      0
##   [54,]      0      0      0      0      0      0      0      0      0
##   [55,]      0      0      0      0      0      0      0      0      0
##   [56,]      0      0      0      0      0      0      0      0      0
##   [57,]      0      0      0      0      0      0      0      0      0
##   [58,]      0      0      0      0      0      0      0      0      0
##   [59,]      0      0      0      0      0      0      0      0      0
##   [60,]      0      0      0      0      0      0      0      0      0
##   [61,]      0      0      0      0      0      0      0      0      0
##   [62,]      0      0      0      0      0      0      0      0      0
##   [63,]      0      0      0      0      0      0      0      0      0
##   [64,]      0      0      0      0      0      0      0      0      0
##   [65,]      0      0      0      0      0      0      0      0      0
##   [66,]      0      0      0      0      0      0      0      0      0
##   [67,]      0      0      0      0      0      0      0      0      0
##   [68,]      0      0      0      0      0      0      0      0      0
##   [69,]      0      0      0      0      0      0      0      0      0
##   [70,]      0      0      0      0      0      0      0      0      0
##   [71,]      0      0      0      0      0      0      0      0      0
##   [72,]      0      0      0      0      0      0      0      0      0
##   [73,]      0      0      0      0      0      0      0      0      0
##   [74,]      0      0      0      0      0      0      0      0      0
##   [75,]      0      0      0      0      0      0      0      0      0
##   [76,]      0      0      0      0      0      0      0      0      0
##   [77,]      0      0      0      0      0      0      0      0      0
##   [78,]      0      0      0      0      0      0      0      0      0
##   [79,]      0      0      0      0      0      0      0      0      0
##   [80,]      0      0      0      0      0      0      0      0      0
##   [81,]      0      0      0      0      0      0      0      0      0
##   [82,]      0      0      0      0      0      0      0      0      0
##   [83,]      0      0      0      0      0      0      0      0      0
##         [,767] [,768] [,769] [,770] [,771] [,772] [,773] [,774] [,775]
##    [1,]     20     21     22     22     22     21     21     21     21
##    [2,]     18     20     20     20     20     20     20     21     22
##    [3,]     17     18     18     18     18     18     20     22     23
##    [4,]     13     15     15     15     16     17     20     22     23
##    [5,]      9     11     11     12     14     16     19     22     23
##    [6,]      5      8      8     10     12     15     18     21     22
##    [7,]      3      5      6      8     11     14     18     20     22
##    [8,]      1      2      3      6     10     13     18     20     21
##    [9,]      0      0      1      4      9     12     17     20     21
##   [10,]      0      0      0      3      9     12     17     19     20
##   [11,]      0      0      0      2      8     11     16     18     20
##   [12,]      0      0      0      0      8     11     15     18     19
##   [13,]      0      0      0      0      8     10     14     17     19
##   [14,]      0      0      0      5      8     10     14     16     18
##   [15,]      0      0      0      4      7      9     13     16     18
##   [16,]      0      0      0      4      6      8     12     15     17
##   [17,]      0      0      0      3      6      8     11     15     17
##   [18,]      0      0      0      3      5      7     11     14     17
##   [19,]      0      0      0      2      5      7     10     14     17
##   [20,]      0      0      0      2      4      7     10     14     17
##   [21,]      0      0      0      2      4      7     10     14     17
##   [22,]      0      0      0      2      4      8     12     14     17
##   [23,]      0      0      0      2      4      8     12     14     17
##   [24,]      0      0      0      2      4      8     12     15     17
##   [25,]      0      0      0      2      5      9     13     15     18
##   [26,]      0      0      0      2      5      9     13     15     18
##   [27,]      0      0      0      2      5      8     12     15     17
##   [28,]      0      0      0      2      4      8     11     14     16
##   [29,]      0      0      0      2      4      8     11     14     16
##   [30,]      0      0      0      2      4      8     11     13     16
##   [31,]      0      0      0      2      4      8     11     13     15
##   [32,]      0      0      0      2      4      8     11     12     15
##   [33,]      0      0      0      2      4      7     10     12     14
##   [34,]      0      0      0      2      4      7     10     12     14
##   [35,]      0      0      0      2      4      7     10     12     14
##   [36,]      0      0      0      2      5      8     10     12     14
##   [37,]      0      0      0      2      5      8     10     12     14
##   [38,]      0      0      0      2      5      8     10     12     14
##   [39,]      0      0      0      2      5      8     10     12     14
##   [40,]      0      0      0      2      5      8     10     12     14
##   [41,]      0      0      0      2      5      8     10     12     14
##   [42,]      0      0      0      2      5      8     10     12     14
##   [43,]      0      0      0      2      5      8     10     12     14
##   [44,]      0      0      0      2      5      8     10     12     14
##   [45,]      0      0      0      2      5      8     10     12     14
##   [46,]      0      0      0      2      5      8     10     12     14
##   [47,]      0      0      0      2      5      8     10     12     14
##   [48,]      0      0      0      2      5      8     10     12     14
##   [49,]      0      0      0      2      5      8     10     12     14
##   [50,]      0      0      0      2      5      8     10     12     14
##   [51,]      0      0      0      3      7      8     10     12     14
##   [52,]      0      0      0      3      7      8     10     12     14
##   [53,]      0      0      0      3      7      8     10     12     14
##   [54,]      0      0      0      3      7      8     10     12     14
##   [55,]      0      0      0      3      7      8     10     12     14
##   [56,]      0      0      0      3      7      8     10     12     14
##   [57,]      0      0      0      3      7      8     10     12     14
##   [58,]      0      0      0      3      7      8     10     12     14
##   [59,]      0      0      0      3      7      8     10     12     14
##   [60,]      0      0      0      3      7      8     10     12     14
##   [61,]      0      0      0      3      6      8     10     12     14
##   [62,]      0      0      0      3      6      8     10     12     14
##   [63,]      0      0      0      3      6      8     10     12     14
##   [64,]      0      0      0      3      6      8     10     12     14
##   [65,]      0      0      0      3      6      8     10     12     14
##   [66,]      0      0      1      4      6      8     10     12     14
##   [67,]      0      0      1      4      6      8     10     12     14
##   [68,]      0      0      1      4      6      8     10     12     14
##   [69,]      0      0      1      4      6      8     10     12     14
##   [70,]      0      0      1      4      6      8     10     12     14
##   [71,]      0      0      1      4      6      8     10     12     14
##   [72,]      0      0      1      4      6      8     10     12     14
##   [73,]      0      0      1      4      6      8     10     12     14
##   [74,]      0      0      1      4      6      8     10     12     14
##   [75,]      0      0      1      4      6      8     10     12     14
##   [76,]      0      0      1      4      6      8     10     12     14
##   [77,]      0      0      1      4      6      8     10     12     14
##   [78,]      0      0      1      4      6      8     10     12     14
##   [79,]      0      0      1      4      6      8     10     12     14
##   [80,]      0      0      2      4      6      8     10     11     13
##   [81,]      0      0      2      4      6      8     10     11     14
##   [82,]      0      0      2      4      6      8     10     11     13
##   [83,]      0      0      2      4      6      8     10     11     13
##         [,776] [,777] [,778] [,779] [,780] [,781] [,782] [,783] [,784]
##    [1,]     21     20     20     20     19     19     19     19     19
##    [2,]     22     22     22     22     22     22     23     24     25
##    [3,]     24     24     24     24     25     25     27     28     29
##    [4,]     24     24     24     24     25     26     28     30     31
##    [5,]     23     23     24     24     25     26     28     30     31
##    [6,]     23     23     24     24     25     26     29     31     32
##    [7,]     22     23     24     24     25     26     29     31     32
##    [8,]     22     23     24     24     25     27     30     32     33
##    [9,]     21     22     23     24     26     27     30     32     33
##   [10,]     21     22     23     24     26     28     31     33     34
##   [11,]     21     22     23     24     26     28     32     33     35
##   [12,]     21     22     23     24     26     28     32     34     35
##   [13,]     20     22     23     25     27     29     32     34     36
##   [14,]     20     21     23     25     27     30     33     35     36
##   [15,]     20     21     23     25     28     30     33     35     37
##   [16,]     19     21     23     26     29     31     34     35     38
##   [17,]     19     21     23     26     29     31     34     36     38
##   [18,]     19     21     23     26     30     32     35     36     39
##   [19,]     19     21     24     27     31     33     35     37     40
##   [20,]     19     22     24     28     32     34     36     39     41
##   [21,]     19     22     24     28     32     34     37     39     42
##   [22,]     19     22     24     28     32     34     37     39     42
##   [23,]     19     22     24     28     32     35     37     40     42
##   [24,]     20     22     25     29     33     35     38     41     43
##   [25,]     20     23     26     29     33     36     39     41     44
##   [26,]     20     23     25     29     33     36     38     41     43
##   [27,]     20     22     25     29     32     35     38     40     42
##   [28,]     19     21     24     28     31     33     36     39     41
##   [29,]     18     21     23     26     30     32     35     37     39
##   [30,]     18     20     23     26     29     31     33     36     38
##   [31,]     17     20     23     26     28     30     32     35     37
##   [32,]     17     19     22     25     27     29     31     33     35
##   [33,]     16     18     21     24     26     28     30     32     34
##   [34,]     16     18     21     23     25     27     29     31     33
##   [35,]     16     17     20     23     25     27     29     31     33
##   [36,]     16     17     20     23     25     27     29     31     32
##   [37,]     16     17     20     23     25     27     29     31     32
##   [38,]     16     17     20     23     25     27     29     31     33
##   [39,]     16     17     20     23     25     27     29     31     33
##   [40,]     16     17     20     23     25     27     29     31     33
##   [41,]     16     17     20     23     25     27     29     31     33
##   [42,]     16     17     20     23     25     27     29     31     33
##   [43,]     16     17     20     23     25     27     29     31     33
##   [44,]     16     18     21     23     25     27     29     30     33
##   [45,]     16     18     21     23     25     27     29     30     33
##   [46,]     16     18     21     23     25     27     28     30     33
##   [47,]     16     18     21     23     25     27     28     30     32
##   [48,]     16     18     21     23     25     27     28     30     32
##   [49,]     16     18     21     23     25     27     28     30     32
##   [50,]     16     18     21     23     25     27     28     29     31
##   [51,]     16     18     21     23     25     27     28     29     31
##   [52,]     16     18     21     23     25     27     28     29     31
##   [53,]     16     18     21     23     25     27     28     30     31
##   [54,]     16     18     21     23     25     27     28     30     31
##   [55,]     16     18     21     23     25     27     28     30     31
##   [56,]     16     18     21     23     25     27     28     30     31
##   [57,]     16     18     21     23     25     27     28     30     31
##   [58,]     16     19     21     23     25     27     28     29     31
##   [59,]     17     19     21     23     25     27     28     29     31
##   [60,]     17     19     21     23     25     26     28     29     31
##   [61,]     17     19     21     23     25     26     28     29     31
##   [62,]     17     19     21     23     24     26     27     29     31
##   [63,]     17     19     21     23     24     26     27     29     31
##   [64,]     17     19     21     23     24     26     27     29     30
##   [65,]     17     19     21     23     24     26     27     29     30
##   [66,]     17     19     21     23     24     26     27     28     30
##   [67,]     17     19     21     22     24     25     27     28     30
##   [68,]     17     19     21     22     24     25     27     28     29
##   [69,]     16     19     21     22     24     25     26     28     29
##   [70,]     16     19     21     22     23     25     26     27     28
##   [71,]     16     19     21     22     23     24     26     27     28
##   [72,]     16     19     20     22     23     24     25     26     27
##   [73,]     17     19     20     21     22     23     25     26     27
##   [74,]     17     18     20     21     22     23     24     26     26
##   [75,]     17     18     20     21     22     22     24     25     26
##   [76,]     17     18     19     20     21     22     23     24     25
##   [77,]     16     18     19     20     21     21     22     24     24
##   [78,]     16     17     19     19     20     21     22     23     24
##   [79,]     16     17     18     19     20     20     21     22     23
##   [80,]     16     17     18     18     19     20     21     22     22
##   [81,]     16     16     17     18     18     19     20     21     21
##   [82,]     15     16     17     17     18     18     19     20     21
##   [83,]     15     16     16     17     17     18     19     19     20
##         [,785] [,786] [,787] [,788] [,789] [,790] [,791] [,792] [,793]
##    [1,]     20     20     20     21     22     22     22     22     22
##    [2,]     25     25     26     27     28     29     30     30     30
##    [3,]     30     30     31     32     34     35     36     36     36
##    [4,]     32     32     32     35     37     38     39     39     39
##    [5,]     32     32     33     36     38     39     39     39     40
##    [6,]     32     33     34     37     39     40     40     41     41
##    [7,]     33     34     35     38     40     41     42     42     43
##    [8,]     34     35     36     39     41     42     43     44     44
##    [9,]     34     35     37     41     42     43     45     45     46
##   [10,]     35     37     39     42     44     45     46     47     47
##   [11,]     36     38     40     43     45     46     47     48     49
##   [12,]     37     39     41     44     46     47     49     50     50
##   [13,]     37     40     42     45     47     49     50     51     52
##   [14,]     38     41     43     46     48     50     51     53     53
##   [15,]     39     42     44     47     49     51     53     54     54
##   [16,]     39     42     45     48     50     52     54     55     56
##   [17,]     40     43     46     49     51     54     55     57     57
##   [18,]     41     44     48     50     53     55     57     59     58
##   [19,]     42     46     49     52     54     57     59     60     60
##   [20,]     44     47     51     54     57     60     60     60     60
##   [21,]     44     48     52     55     57     59     60     60     60
##   [22,]     45     48     52     55     57     59     60     60     60
##   [23,]     45     49     53     56     58     60     62     62     60
##   [24,]     48     52     54     58     60     64     68     71     61
##   [25,]     48     52     55     59     60     62     66     63     61
##   [26,]     47     51     54     56     58     60     61     61     60
##   [27,]     46     50     53     55     57     58     59     60     60
##   [28,]     44     48     50     53     55     57     58     60     60
##   [29,]     43     46     48     50     53     55     57     60     60
##   [30,]     41     44     47     49     51     53     55     57     60
##   [31,]     40     43     45     47     49     51     53     55     58
##   [32,]     38     41     43     45     47     49     52     54     56
##   [33,]     37     40     42     44     46     47     50     53     55
##   [34,]     36     39     41     43     45     46     49     52     53
##   [35,]     35     38     40     42     44     46     48     51     53
##   [36,]     35     38     40     42     44     46     48     51     52
##   [37,]     35     38     40     42     43     45     48     50     52
##   [38,]     36     38     40     42     43     45     47     49     51
##   [39,]     36     38     40     41     43     45     47     49     50
##   [40,]     36     38     39     41     43     44     46     48     49
##   [41,]     36     38     39     41     42     44     46     47     49
##   [42,]     36     38     39     41     42     43     45     46     47
##   [43,]     36     37     39     40     41     42     44     46     46
##   [44,]     35     37     38     39     41     42     43     45     46
##   [45,]     35     37     38     39     40     41     42     44     44
##   [46,]     35     36     37     38     39     40     42     42     43
##   [47,]     34     35     36     37     38     40     41     42     43
##   [48,]     34     35     36     37     37     39     40     41     42
##   [49,]     33     34     35     36     37     38     40     41     42
##   [50,]     33     34     35     36     37     38     40     41     42
##   [51,]     32     33     35     36     37     38     40     41     42
##   [52,]     32     33     35     36     37     38     40     41     42
##   [53,]     32     34     35     36     37     39     40     42     42
##   [54,]     32     34     35     36     37     39     40     42     43
##   [55,]     32     34     35     36     37     39     40     42     43
##   [56,]     32     34     35     36     37     39     40     42     42
##   [57,]     32     33     35     36     37     39     40     41     42
##   [58,]     32     33     35     36     37     39     40     41     42
##   [59,]     32     33     35     35     37     38     40     41     42
##   [60,]     32     33     34     35     37     39     40     41     42
##   [61,]     32     33     34     35     37     38     40     40     41
##   [62,]     32     33     34     35     37     38     39     40     41
##   [63,]     32     33     34     35     36     38     39     40     40
##   [64,]     32     32     33     35     36     37     39     39     40
##   [65,]     31     32     33     34     36     37     38     39     39
##   [66,]     31     32     33     34     35     36     37     38     39
##   [67,]     30     31     32     33     35     36     37     38     39
##   [68,]     30     31     32     33     34     35     36     37     38
##   [69,]     30     31     32     32     34     35     36     37     37
##   [70,]     29     30     31     32     33     34     35     36     37
##   [71,]     29     30     31     32     33     34     35     35     36
##   [72,]     28     29     30     31     32     33     34     34     35
##   [73,]     28     28     29     30     31     32     33     34     35
##   [74,]     27     28     29     30     31     32     32     33     34
##   [75,]     26     27     28     29     30     31     31     32     33
##   [76,]     26     26     27     28     29     30     31     31     32
##   [77,]     25     26     26     28     28     29     30     30     31
##   [78,]     24     25     26     27     28     28     29     30     31
##   [79,]     24     24     25     26     27     28     28     29     30
##   [80,]     23     24     24     25     26     27     27     28     29
##   [81,]     22     23     24     24     25     26     26     27     28
##   [82,]     21     22     23     24     24     25     25     26     27
##   [83,]     21     21     22     23     24     24     25     25     26
##         [,794] [,795] [,796] [,797] [,798] [,799] [,800] [,801] [,802]
##    [1,]     22     22     22     22     22     23     24     24     24
##    [2,]     30     30     30     30     30     31     32     33     33
##    [3,]     36     36     36     36     36     38     39     40     40
##    [4,]     39     39     39     39     39     41     43     44     44
##    [5,]     40     40     40     40     41     43     45     45     46
##    [6,]     41     41     41     41     42     44     46     46     46
##    [7,]     43     43     43     43     44     46     47     47     47
##    [8,]     44     44     44     44     45     47     48     48     48
##    [9,]     46     46     46     46     46     48     49     49     49
##   [10,]     47     47     47     47     47     49     50     50     50
##   [11,]     49     49     49     49     49     50     51     51     51
##   [12,]     50     50     50     50     50     52     52     52     52
##   [13,]     51     51     51     51     51     53     53     53     53
##   [14,]     52     52     52     52     52     53     53     54     54
##   [15,]     54     54     54     54     54     54     54     55     55
##   [16,]     55     55     55     55     55     55     56     56     56
##   [17,]     56     57     57     57     57     57     57     57     57
##   [18,]     58     58     58     58     58     58     58     58     58
##   [19,]     59     60     59     59     59     59     59     59     59
##   [20,]     60     60     60     60     60     60     60     60     59
##   [21,]     60     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     60     60     60     60     60     60     60     60     60
##   [24,]     60     60     60     60     60     60     60     60     60
##   [25,]     60     60     60     60     60     60     60     60     60
##   [26,]     60     60     60     60     60     60     60     60     60
##   [27,]     60     60     60     60     60     60     60     60     60
##   [28,]     60     60     60     60     60     60     60     60     60
##   [29,]     60     60     60     60     60     60     60     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     59     60     60     60     60     60     60     60     60
##   [32,]     58     58     59     60     60     60     60     60     60
##   [33,]     56     58     59     60     60     60     60     60     60
##   [34,]     55     56     58     59     60     60     60     60     60
##   [35,]     54     56     57     58     59     59     60     60     60
##   [36,]     54     55     56     57     58     59     59     60     60
##   [37,]     53     54     55     56     57     58     59     60     60
##   [38,]     52     53     54     55     56     57     58     59     59
##   [39,]     51     53     53     54     55     56     57     58     58
##   [40,]     50     51     53     54     55     56     56     57     57
##   [41,]     49     50     51     53     54     55     55     56     56
##   [42,]     49     49     50     52     53     53     54     55     56
##   [43,]     47     48     49     51     52     53     53     54     55
##   [44,]     46     47     48     49     51     52     53     53     54
##   [45,]     45     46     47     48     50     51     52     53     53
##   [46,]     44     45     46     48     49     50     51     52     52
##   [47,]     44     45     46     47     48     49     50     51     52
##   [48,]     43     44     45     46     48     49     49     50     51
##   [49,]     43     44     45     46     47     49     49     51     52
##   [50,]     43     44     45     46     48     49     50     51     52
##   [51,]     43     44     45     47     48     49     50     52     53
##   [52,]     43     44     45     47     49     50     51     52     53
##   [53,]     44     45     46     48     49     50     51     53     53
##   [54,]     44     45     47     48     49     50     51     53     54
##   [55,]     44     45     46     48     49     50     51     52     53
##   [56,]     44     45     46     48     49     50     51     52     53
##   [57,]     43     44     46     48     48     49     50     51     52
##   [58,]     43     44     46     47     48     49     49     50     51
##   [59,]     43     44     45     46     47     48     49     49     50
##   [60,]     42     43     44     46     46     47     48     49     49
##   [61,]     42     42     43     45     45     46     47     48     48
##   [62,]     41     42     43     44     45     46     46     47     48
##   [63,]     41     41     42     44     44     45     46     46     48
##   [64,]     40     41     42     43     44     45     45     46     47
##   [65,]     40     41     42     43     44     44     45     46     47
##   [66,]     40     40     42     42     43     44     45     46     47
##   [67,]     39     40     41     42     43     44     44     45     46
##   [68,]     39     40     41     42     42     43     44     45     46
##   [69,]     38     39     40     41     42     42     43     44     45
##   [70,]     37     39     40     40     41     42     43     44     45
##   [71,]     37     38     39     40     41     42     42     43     44
##   [72,]     36     37     39     39     40     41     42     43     44
##   [73,]     35     37     38     39     40     41     42     42     44
##   [74,]     35     36     37     38     39     40     41     42     43
##   [75,]     34     35     37     38     39     39     40     41     42
##   [76,]     33     34     36     37     38     39     39     41     42
##   [77,]     32     34     35     36     37     38     39     40     41
##   [78,]     32     33     35     35     36     37     38     40     41
##   [79,]     31     32     34     35     35     36     37     39     40
##   [80,]     30     31     33     34     35     35     36     38     39
##   [81,]     29     30     32     33     34     35     35     37     38
##   [82,]     29     30     31     32     33     34     35     36     37
##   [83,]     28     29     30     31     32     33     34     35     37
##         [,803] [,804] [,805] [,806] [,807] [,808] [,809] [,810] [,811]
##    [1,]     25     25     25     25     26     27     28     29     30
##    [2,]     34     34     34     34     35     36     37     38     39
##    [3,]     41     41     41     41     42     43     44     45     46
##    [4,]     45     45     45     45     45     47     48     49     50
##    [5,]     46     46     46     46     46     49     50     50     51
##    [6,]     46     46     46     47     47     49     51     51     51
##    [7,]     47     47     47     48     48     50     51     52     52
##    [8,]     48     48     48     48     49     51     52     52     52
##    [9,]     49     49     49     49     50     52     52     53     53
##   [10,]     50     50     50     50     51     52     53     53     53
##   [11,]     51     51     51     51     52     53     53     53     54
##   [12,]     52     52     52     53     53     53     53     54     54
##   [13,]     53     53     53     54     54     54     54     55     55
##   [14,]     54     54     54     54     55     55     55     56     56
##   [15,]     55     55     55     55     56     56     56     57     57
##   [16,]     56     56     56     57     57     57     58     58     58
##   [17,]     57     57     58     58     58     58     58     59     59
##   [18,]     58     58     58     58     59     59     59     59     60
##   [19,]     59     59     59     59     59     59     59     59     60
##   [20,]     59     59     59     59     60     60     60     60     60
##   [21,]     60     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     60     60     60     60     60     60     60     60     60
##   [24,]     60     60     60     60     60     60     60     60     60
##   [25,]     60     60     60     60     60     60     60     60     60
##   [26,]     60     60     60     60     60     60     60     60     60
##   [27,]     60     60     60     60     60     60     60     60     60
##   [28,]     60     60     60     60     60     60     60     60     60
##   [29,]     60     60     60     60     60     60     60     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     60     60     60     60     60     60     60     60     60
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     60     60     60     60
##   [34,]     60     60     60     60     60     60     60     60     60
##   [35,]     60     60     60     60     60     60     60     60     60
##   [36,]     60     60     60     60     60     60     60     60     60
##   [37,]     60     60     60     60     60     60     60     60     60
##   [38,]     59     60     60     60     60     60     60     60     60
##   [39,]     59     59     60     60     59     59     59     60     60
##   [40,]     58     59     59     59     59     59     59     59     60
##   [41,]     57     58     58     58     58     59     59     59     59
##   [42,]     56     57     58     58     58     58     59     59     60
##   [43,]     55     56     57     57     58     58     58     59     59
##   [44,]     54     56     56     57     57     58     58     59     59
##   [45,]     54     55     56     56     57     57     58     59     59
##   [46,]     53     55     56     56     57     57     58     59     59
##   [47,]     53     54     55     56     56     57     58     59     60
##   [48,]     53     54     55     56     57     58     59     60     63
##   [49,]     53     55     56     57     58     59     60     64     69
##   [50,]     54     56     57     58     60     61     62     70     78
##   [51,]     54     56     57     59     60     63     67     78     88
##   [52,]     55     57     58     60     60     65     72     85     98
##   [53,]     55     57     59     60     60     68     75     88    103
##   [54,]     55     57     58     59     60     63     71     86     98
##   [55,]     55     56     57     58     59     60     65     78     83
##   [56,]     54     56     56     57     58     59     60     64     66
##   [57,]     53     55     56     56     57     58     59     60     60
##   [58,]     53     54     54     55     56     57     58     59     59
##   [59,]     51     53     53     54     55     56     57     58     58
##   [60,]     50     52     52     53     54     55     56     57     57
##   [61,]     50     51     51     52     53     54     55     56     57
##   [62,]     49     50     51     52     52     53     54     55     56
##   [63,]     49     49     50     51     52     52     54     55     56
##   [64,]     48     49     50     51     51     52     53     55     56
##   [65,]     48     49     50     51     51     52     53     55     56
##   [66,]     48     49     49     50     51     52     53     54     55
##   [67,]     47     48     49     50     51     51     53     54     55
##   [68,]     47     48     48     49     50     51     52     53     54
##   [69,]     46     47     48     49     49     51     52     53     54
##   [70,]     46     47     48     48     49     50     51     52     53
##   [71,]     45     46     47     48     49     50     51     52     53
##   [72,]     45     46     47     48     49     50     51     52     53
##   [73,]     45     46     47     48     49     50     51     52     53
##   [74,]     44     45     46     47     48     49     51     52     53
##   [75,]     44     45     46     46     47     49     50     51     52
##   [76,]     43     44     45     46     47     48     50     51     52
##   [77,]     42     43     44     45     46     48     49     50     51
##   [78,]     42     43     44     45     46     47     48     49     50
##   [79,]     41     42     43     44     45     46     47     48     49
##   [80,]     40     41     42     43     44     45     46     47     48
##   [81,]     39     40     41     42     43     44     46     47     48
##   [82,]     38     39     40     41     42     44     45     46     47
##   [83,]     38     39     40     41     42     43     45     46     47
##         [,812] [,813] [,814] [,815] [,816] [,817] [,818] [,819] [,820]
##    [1,]     31     32     32     33     33     34     35     36     37
##    [2,]     39     40     40     41     41     42     42     43     43
##    [3,]     46     46     47     47     47     48     48     48     48
##    [4,]     50     49     50     50     50     51     51     51     50
##    [5,]     51     50     51     51     51     51     52     52     51
##    [6,]     51     50     51     52     52     52     52     53     52
##    [7,]     52     51     52     53     53     53     53     53     53
##    [8,]     52     52     53     53     54     54     54     54     54
##    [9,]     53     53     54     54     54     55     55     55     56
##   [10,]     54     54     55     55     55     56     56     56     57
##   [11,]     54     54     55     56     56     56     57     58     59
##   [12,]     55     55     56     56     57     57     58     59     60
##   [13,]     56     56     57     57     58     58     59     60     60
##   [14,]     56     57     58     58     58     59     59     60     60
##   [15,]     58     58     59     59     59     60     60     60     60
##   [16,]     59     60     60     60     60     60     60     60     60
##   [17,]     60     60     60     60     60     60     60     60     60
##   [18,]     60     60     60     60     60     60     60     60     60
##   [19,]     60     60     60     60     60     60     60     60     60
##   [20,]     60     60     60     60     60     60     60     60     60
##   [21,]     60     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     60     60     60     60     60     60     60     60     60
##   [24,]     60     60     60     60     60     60     60     60     60
##   [25,]     60     60     60     60     60     60     60     60     60
##   [26,]     60     60     60     60     60     60     60     60     60
##   [27,]     60     60     60     60     60     60     60     60     60
##   [28,]     60     60     60     60     60     60     60     60     60
##   [29,]     60     60     60     60     60     60     60     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     60     60     60     60     60     60     60     60     60
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     60     60     60     60
##   [34,]     60     60     60     60     60     60     60     60     60
##   [35,]     60     60     60     60     60     60     60     60     60
##   [36,]     60     60     60     60     60     60     60     60     60
##   [37,]     60     60     60     60     60     60     60     60     60
##   [38,]     60     60     60     60     60     60     60     60     60
##   [39,]     60     60     60     60     60     60     60     60     60
##   [40,]     60     60     60     60     60     60     60     60     60
##   [41,]     60     60     60     60     60     60     60     60     60
##   [42,]     60     60     60     60     60     60     60     60     60
##   [43,]     60     60     60     60     60     60     60     60     60
##   [44,]     60     60     60     60     60     60     60     60     60
##   [45,]     60     60     60     60     60     60     60     60     60
##   [46,]     60     60     60     60     60     60     60     60     60
##   [47,]     60     60     60     60     60     60     60     60     60
##   [48,]     64     64     65     67     72     68     63     60     66
##   [49,]     73     76     79     83     85     83     78     80     81
##   [50,]     84     89     94     97     98     98     95     97    102
##   [51,]     96    103    110    111    113    113    113    114    121
##   [52,]    108    117    120    121    121    121    120    121    120
##   [53,]    121    120    121    121    121    121    121    121    121
##   [54,]    107    121    121    121    121    121    121    121    121
##   [55,]     89     88    102    113    121    121    121    121    121
##   [56,]     66     60     76     84    109    121    121    121    121
##   [57,]     60     61     60     60     68    100    101    110    121
##   [58,]     59     59     60     60     60     60     60     60     93
##   [59,]     58     59     59     59     60     60     60     60     60
##   [60,]     58     58     59     59     60     60     60     60     60
##   [61,]     57     58     59     59     60     60     60     60     60
##   [62,]     57     58     59     59     60     60     60     60     60
##   [63,]     56     57     58     59     60     60     60     60     60
##   [64,]     56     57     58     59     60     60     60     60     60
##   [65,]     56     57     58     60     60     60     60     60     60
##   [66,]     56     57     58     59     60     60     60     60     60
##   [67,]     56     56     57     58     60     60     60     60     60
##   [68,]     55     56     57     58     59     60     60     60     60
##   [69,]     54     55     56     58     59     60     60     60     60
##   [70,]     54     55     56     57     58     59     60     60     60
##   [71,]     54     55     56     57     58     59     60     60     60
##   [72,]     54     55     56     57     59     60     60     60     60
##   [73,]     54     55     56     58     60     60     60     60     60
##   [74,]     54     55     56     57     59     60     60     60     60
##   [75,]     53     54     55     57     58     59     60     60     60
##   [76,]     53     53     55     56     58     58     59     60     60
##   [77,]     52     53     54     56     57     58     59     60     60
##   [78,]     51     52     53     55     56     57     58     59     60
##   [79,]     50     51     53     54     55     56     57     58     59
##   [80,]     49     50     52     53     54     55     56     57     58
##   [81,]     49     50     51     53     54     55     56     57     58
##   [82,]     48     49     51     52     53     54     55     56     57
##   [83,]     48     49     50     52     53     54     55     56     57
##         [,821] [,822] [,823] [,824] [,825] [,826] [,827] [,828] [,829]
##    [1,]     38     39     40     42     45     49     52     56     58
##    [2,]     44     45     46     48     50     52     55     58     60
##    [3,]     48     49     50     52     54     56     58     60     62
##    [4,]     50     51     51     53     55     57     59     61     62
##    [5,]     52     52     52     55     56     57     60     61     62
##    [6,]     53     53     53     56     57     58     60     61     61
##    [7,]     54     54     54     56     57     58     60     61     61
##    [8,]     55     55     55     57     58     58     60     61     60
##    [9,]     56     56     57     57     58     59     60     60     60
##   [10,]     58     57     58     58     59     60     60     60     60
##   [11,]     59     59     59     59     60     60     60     60     60
##   [12,]     60     60     60     60     60     60     60     60     60
##   [13,]     60     60     60     60     60     60     60     60     60
##   [14,]     60     60     60     60     60     60     60     60     60
##   [15,]     60     60     60     60     60     60     60     60     60
##   [16,]     60     60     60     60     60     60     60     60     60
##   [17,]     60     60     60     60     60     60     60     60     60
##   [18,]     60     60     60     60     60     60     60     60     60
##   [19,]     60     60     60     60     60     60     60     60     60
##   [20,]     60     60     60     60     60     60     60     60     60
##   [21,]     60     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     60     60     60     60     60     60     60     60     60
##   [24,]     60     60     60     60     60     60     60     60     60
##   [25,]     60     60     60     60     60     60     60     60     60
##   [26,]     60     60     60     60     60     60     60     60     60
##   [27,]     60     60     60     60     60     60     60     60     60
##   [28,]     60     60     60     60     60     60     60     60     60
##   [29,]     60     60     60     60     60     60     60     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     60     60     60     60     60     60     60     60     60
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     60     60     60     60
##   [34,]     60     60     60     60     60     60     60     60     60
##   [35,]     60     60     60     60     60     60     60     60     60
##   [36,]     60     60     60     60     60     60     60     60     60
##   [37,]     60     60     60     60     60     60     60     60     60
##   [38,]     60     60     60     60     60     60     60     60     60
##   [39,]     60     60     60     60     60     60     60     60     60
##   [40,]     60     60     60     60     60     60     60     60     60
##   [41,]     60     60     60     60     60     60     60     60     60
##   [42,]     60     60     60     60     60     60     60     60     60
##   [43,]     60     60     60     60     60     60     60     60     60
##   [44,]     60     60     60     60     60     60     60     60     60
##   [45,]     60     60     60     60     60     60     60     60     60
##   [46,]     60     60     60     60     60     60     60     60     66
##   [47,]     60     60     60     60     64     60     71     77     78
##   [48,]     69     69     68     78     78     84     88     94     90
##   [49,]     88     86     88     93     96    101    108    110    107
##   [50,]    105    104    105    108    112    117    129    131    127
##   [51,]    121    121    121    118    121    157    158    161    147
##   [52,]    121    121    140    121    182    182    182    182    172
##   [53,]    121    121    148    175    175    180    182    182    182
##   [54,]    121    121    144    162    171    182    182    182    182
##   [55,]    121    121    136    151    160    169    178    182    182
##   [56,]    121    121    126    138    147    156    164    167    176
##   [57,]    121    118    119    126    134    143    149    151    163
##   [58,]    121    113    107    114    121    130    135    133    151
##   [59,]     76     88     92    101    111    120    123    121    139
##   [60,]     60     60     77     89    103    121    115    119    128
##   [61,]     60     60     60     68     83     89    101    109    121
##   [62,]     60     60     60     60     60     71     81     92    110
##   [63,]     60     60     60     60     60     60     71     83    105
##   [64,]     60     61     61     60     60     60     60     73    109
##   [65,]     60     63     64     63     60     60     60     60     89
##   [66,]     60     64     67     68     66     63     60     60     60
##   [67,]     60     67     72     74     74     73     73     71     60
##   [68,]     60     69     77     81     84     86     89     93     91
##   [69,]     60     73     83     89     95    101    106    117    110
##   [70,]     70     77     88     95    103    111    118    120    121
##   [71,]     73     85     92    100    109    121    120    121    122
##   [72,]     72     83     91     99    107    114    121    121    122
##   [73,]     70     81     89     96    104    111    117    121    124
##   [74,]     69     80     87     95    102    109    115    121    125
##   [75,]     66     78     85     92     99    107    114    121    126
##   [76,]     67     76     83     90     97    105    112    120    129
##   [77,]     65     75     82     90     98    106    114    121    128
##   [78,]     62     72     80     89     97    106    117    120    121
##   [79,]     60     68     78     88     98    108    120    121    121
##   [80,]     60     60     74     86     96    108    121    121    121
##   [81,]     60     60     70     81     91    101    114    121    121
##   [82,]     59     60     67     75     84     93    108    121    121
##   [83,]     59     60     63     69     77     87    101    114    121
##         [,830] [,831] [,832] [,833] [,834] [,835] [,836] [,837] [,838]
##    [1,]     60     61     62     63     66     68     70     72     72
##    [2,]     62     63     63     65     68     72     75     77     77
##    [3,]     64     65     64     66     70     74     77     79     79
##    [4,]     64     65     64     65     68     72     75     77     78
##    [5,]     64     64     63     63     65     68     71     73     73
##    [6,]     63     62     62     62     63     64     66     67     68
##    [7,]     61     61     61     61     61     61     62     63     63
##    [8,]     60     60     61     61     60     60     60     61     61
##    [9,]     60     60     60     60     60     60     60     60     60
##   [10,]     60     60     60     60     60     60     60     60     60
##   [11,]     60     60     60     60     60     60     60     60     60
##   [12,]     60     60     60     60     60     60     60     60     60
##   [13,]     60     60     60     60     60     60     60     60     60
##   [14,]     60     60     60     60     60     60     60     60     60
##   [15,]     60     60     60     60     60     60     60     60     61
##   [16,]     60     60     60     60     60     60     60     60     61
##   [17,]     60     60     60     60     60     60     60     61     62
##   [18,]     60     60     60     60     60     60     60     61     62
##   [19,]     60     60     60     60     60     60     61     61     64
##   [20,]     60     60     60     60     60     60     61     62     64
##   [21,]     60     60     60     60     60     60     61     62     65
##   [22,]     60     60     60     60     60     60     61     63     66
##   [23,]     60     60     60     60     60     60     61     64     68
##   [24,]     60     60     60     60     60     60     61     64     69
##   [25,]     60     60     60     60     60     60     62     64     69
##   [26,]     60     60     60     60     60     60     62     64     67
##   [27,]     60     60     60     60     60     60     61     63     65
##   [28,]     60     60     60     60     60     60     60     60     61
##   [29,]     60     60     60     60     60     60     60     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     60     60     60     60     60     60     60     60     60
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     60     60     60     60
##   [34,]     60     60     60     60     60     60     60     60     60
##   [35,]     60     60     60     60     60     60     60     60     60
##   [36,]     60     60     60     60     60     60     60     60     60
##   [37,]     60     60     60     60     60     60     60     60     60
##   [38,]     60     60     60     60     60     60     60     60     60
##   [39,]     60     60     60     60     60     60     60     60     60
##   [40,]     60     60     60     60     60     60     60     60     60
##   [41,]     60     60     60     60     60     60     60     60     60
##   [42,]     60     60     60     60     60     60     60     60     60
##   [43,]     60     60     60     60     60     60     60     60     60
##   [44,]     60     60     60     60     60     60     60     60     60
##   [45,]     61     60     60     60     60     60     60     60     60
##   [46,]     64     62     60     60     60     60     60     61     60
##   [47,]     72     65     60     60     60     60     60     64     63
##   [48,]     82     73     67     60     60     60     60     69     70
##   [49,]     95     85     78     71     60     60     60     77     79
##   [50,]    111     99     94     88     82     73     78     88     86
##   [51,]    121    112    110    107     99     90     93     98     96
##   [52,]    138    121    121    121    110    101    101    104    106
##   [53,]    163    156    147    135    126    116    115    112    113
##   [54,]    182    182    169    154    142    134    123    119    119
##   [55,]    182    182    182    169    157    147    133    121    131
##   [56,]    182    182    182    182    172    162    151    152    153
##   [57,]    176    182    182    182    182    177    173    176    174
##   [58,]    167    175    182    182    182    182    182    182    182
##   [59,]    158    169    181    182    182    182    182    182    182
##   [60,]    147    160    171    182    182    182    182    182    182
##   [61,]    135    146    159    168    175    182    182    182    182
##   [62,]    121    131    148    160    170    181    182    182    182
##   [63,]    120    121    142    157    170    182    182    182    171
##   [64,]    121    131    140    153    168    182    182    182    158
##   [65,]    121    127    139    152    166    182    182    157    142
##   [66,]     75    112    127    141    158    178    170    147    121
##   [67,]     89     96    111    121    142    153    150    133    121
##   [68,]     95    104    113    119    126    133    130    121    124
##   [69,]    111    114    117    119    120    122    121    123    121
##   [70,]    120    119    120    121    121    121    121    121    121
##   [71,]    121    121    121    121    121    121    121    121    121
##   [72,]    124    124    121    121    121    121    121    121    121
##   [73,]    126    128    128    130    127    121    121    121    121
##   [74,]    128    131    135    138    140    140    133    121    121
##   [75,]    131    136    142    148    156    164    169    149    134
##   [76,]    135    142    149    157    170    182    179    182    182
##   [77,]    135    143    151    160    174    181    182    182    182
##   [78,]    131    140    149    157    170    182    182    182    182
##   [79,]    124    135    145    155    169    181    182    182    182
##   [80,]    121    133    143    153    168    182    182    182    182
##   [81,]    130    136    144    152    166    179    182    182    182
##   [82,]    129    137    144    151    162    172    177    182    182
##   [83,]    128    135    142    149    159    168    174    178    182
##         [,839] [,840] [,841] [,842] [,843] [,844] [,845] [,846] [,847]
##    [1,]     72     70     67     64     61     57     54     52     50
##    [2,]     76     74     71     68     65     62     59     57     55
##    [3,]     78     76     73     70     67     64     62     61     59
##    [4,]     76     74     71     69     66     64     62     61     60
##    [5,]     72     70     67     65     63     62     61     60     60
##    [6,]     67     65     63     62     61     60     60     60     60
##    [7,]     63     62     61     60     60     60     60     60     60
##    [8,]     61     60     60     60     60     60     60     60     60
##    [9,]     60     60     60     60     60     60     60     60     60
##   [10,]     60     60     60     60     60     60     60     60     60
##   [11,]     60     60     60     60     60     60     60     60     60
##   [12,]     60     60     60     60     60     60     60     60     60
##   [13,]     60     60     60     60     60     60     60     60     60
##   [14,]     61     60     60     60     60     60     60     60     60
##   [15,]     61     62     61     61     61     61     61     60     60
##   [16,]     62     62     62     62     62     62     61     60     60
##   [17,]     63     63     63     63     63     64     63     60     60
##   [18,]     64     65     65     65     66     67     67     69     70
##   [19,]     66     66     67     67     68     70     72     74     79
##   [20,]     67     68     69     71     73     75     78     83     88
##   [21,]     68     71     73     76     78     81     85     91     96
##   [22,]     70     74     77     81     84     87     92     97    101
##   [23,]     71     75     78     82     85     88     93     98    101
##   [24,]     73     75     78     81     84     87     91     95     98
##   [25,]     72     75     77     80     82     84     88     91     93
##   [26,]     70     72     74     76     78     80     83     84     86
##   [27,]     67     68     70     71     72     74     73     73     74
##   [28,]     62     63     63     64     64     65     60     60     60
##   [29,]     60     61     61     61     60     61     61     60     60
##   [30,]     60     60     60     60     60     60     60     60     60
##   [31,]     60     60     60     60     60     60     60     60     60
##   [32,]     60     60     60     60     60     60     60     60     60
##   [33,]     60     60     60     60     60     60     60     60     60
##   [34,]     60     60     60     60     60     60     60     60     60
##   [35,]     60     60     60     60     60     60     60     60     60
##   [36,]     60     60     60     60     60     60     60     60     60
##   [37,]     60     60     60     60     60     60     60     60     60
##   [38,]     60     60     60     60     60     60     60     60     60
##   [39,]     60     60     60     60     60     60     60     60     60
##   [40,]     60     60     60     60     60     60     60     60     60
##   [41,]     60     60     60     60     60     60     60     60     60
##   [42,]     60     60     60     60     60     60     60     60     60
##   [43,]     60     60     60     60     60     60     60     60     60
##   [44,]     60     60     60     60     60     60     60     60     60
##   [45,]     60     60     60     60     60     60     60     60     60
##   [46,]     60     60     60     60     61     60     60     60     60
##   [47,]     60     60     63     60     69     65     60     60     60
##   [48,]     68     68     70     75     80     77     72     70     70
##   [49,]     78     82     83     86     90     90     88     91     89
##   [50,]     85     89     90     93     98     99     99    102    102
##   [51,]     96     99    101    104    109    113    117    117    118
##   [52,]    108    110    112    115    120    121    138    137    142
##   [53,]    115    118    119    124    137    153    170    160    163
##   [54,]    121    134    136    147    167    182    176    182    182
##   [55,]    146    156    158    166    179    181    186    190    191
##   [56,]    168    182    182    176    178    182    192    200    206
##   [57,]    182    180    181    182    181    188    199    211    224
##   [58,]    181    182    182    182    182    196    208    220    243
##   [59,]    182    182    182    182    182    191    202    211    223
##   [60,]    182    182    182    182    182    182    192    195    207
##   [61,]    182    182    182    182    173    178    182    182    195
##   [62,]    177    173    166    159    157    163    171    179    182
##   [63,]    162    152    146    139    141    148    163    176    180
##   [64,]    142    130    127    124    126    135    159    178    180
##   [65,]    121    125    122    121    122    121    157    182    181
##   [66,]    123    122    122    131    142    170    167    182    185
##   [67,]    121    121    134    162    182    175    182    184    190
##   [68,]    121    125    150    182    180    182    183    188    196
##   [69,]    121    135    153    182    182    182    186    192    200
##   [70,]    121    130    145    164    177    182    185    191    200
##   [71,]    121    121    130    153    163    173    182    182    188
##   [72,]    121    121    126    145    155    164    171    178    182
##   [73,]    121    121    121    133    142    152    160    168    178
##   [74,]    121    121    121    121    130    138    148    157    170
##   [75,]    121    121    121    121    121    126    137    146    158
##   [76,]    150    121    121    121    121    121    127    135    146
##   [77,]    182    167    129    121    121    121    121    125    134
##   [78,]    182    182    167    121    121    121    121    121    121
##   [79,]    182    183    183    171    162    139    131    121    121
##   [80,]    182    183    184    185    184    182    182    157    143
##   [81,]    182    184    186    188    187    187    185    182    171
##   [82,]    182    185    189    192    192    194    194    195    189
##   [83,]    182    186    191    195    198    201    203    207    205
##         [,848] [,849] [,850] [,851] [,852] [,853] [,854] [,855] [,856]
##    [1,]     48     47     46     44     41     38     34     31     29
##    [2,]     54     53     52     50     47     43     40     37     35
##    [3,]     58     58     57     54     51     47     44     42     39
##    [4,]     60     60     59     57     54     49     46     44     41
##    [5,]     60     60     60     59     56     51     48     45     43
##    [6,]     60     60     60     59     56     52     49     46     45
##    [7,]     60     60     60     59     56     52     50     48     47
##    [8,]     60     60     60     59     56     53     52     50     49
##    [9,]     60     60     60     59     57     55     54     52     51
##   [10,]     60     60     60     60     58     57     55     54     53
##   [11,]     60     60     60     60     60     59     57     56     55
##   [12,]     60     60     61     60     60     60     58     58     57
##   [13,]     60     60     64     64     61     60     59     59     59
##   [14,]     60     60     68     69     66     60     60     60     60
##   [15,]     60     67     74     76     74     68     63     60     60
##   [16,]     60     77     82     84     83     78     72     66     60
##   [17,]     70     81     86     89     89     84     78     71     67
##   [18,]     77     88     93     97     99     93     87     79     73
##   [19,]     85     94    100    105    108    103     96     86     78
##   [20,]     93    100    107    116    117    112    105     93     81
##   [21,]    101    107    115    121    121    121    114     99     85
##   [22,]    106    111    118    121    121    121    121    100     82
##   [23,]    105    109    113    119    121    121    121    101     87
##   [24,]    101    105    109    116    121    121    110    102     94
##   [25,]     96     99    103    111    117    121    113    107    103
##   [26,]     88     92     96    106    115    121    119    116    113
##   [27,]     75     82     87    100    112    121    121    121    120
##   [28,]     60     72     75     94    108    114    121    120    121
##   [29,]     60     60     66     87    101    107    111    115    119
##   [30,]     60     60     71     84     95     99    103    105    109
##   [31,]     60     60     70     81     88     91     94     96     99
##   [32,]     60     60     68     75     80     83     85     86     88
##   [33,]     60     60     65     70     72     74     75     76     76
##   [34,]     60     60     60     63     64     65     66     66     64
##   [35,]     60     60     60     60     61     61     62     61     60
##   [36,]     60     60     60     60     60     60     60     60     60
##   [37,]     60     60     60     60     60     60     60     60     60
##   [38,]     60     60     60     60     60     60     60     60     60
##   [39,]     60     60     60     60     60     60     60     60     60
##   [40,]     60     60     60     60     60     60     60     60     60
##   [41,]     60     60     60     60     60     60     60     60     60
##   [42,]     60     60     60     60     60     60     60     60     60
##   [43,]     60     60     60     60     60     60     60     60     60
##   [44,]     60     60     60     60     60     60     60     60     60
##   [45,]     60     60     60     60     60     60     60     60     60
##   [46,]     60     60     60     60     60     60     60     60     60
##   [47,]     60     60     60     60     60     60     60     60     60
##   [48,]     65     64     71     64     60     60     60     60     60
##   [49,]     85     84     83     75     70     65     60     60     60
##   [50,]    103     96     91     86     81     74     66     60     60
##   [51,]    122    112    104     99     96     86     76     66     67
##   [52,]    135    125    121    117    121    103     91     82     86
##   [53,]    155    146    136    131    127    118    106     99    100
##   [54,]    172    166    159    158    157    138    121    115    113
##   [55,]    190    183    177    178    181    172    146    121    120
##   [56,]    212    199    182    187    184    181    182    121    121
##   [57,]    235    220    208    196    188    182    161    143    136
##   [58,]    239    243    227    213    199    182    172    161    163
##   [59,]    237    243    243    227    213    198    182    176    173
##   [60,]    225    243    243    243    236    220    210    195    189
##   [61,]    215    234    243    243    243    243    231    217    209
##   [62,]    198    223    243    243    243    243    243    237    227
##   [63,]    182    202    221    243    243    243    243    243    243
##   [64,]    182    182    192    224    239    243    243    243    243
##   [65,]    182    182    210    218    231    238    243    243    243
##   [66,]    189    197    209    220    229    236    240    243    243
##   [67,]    198    208    216    224    231    238    242    243    243
##   [68,]    207    220    229    238    240    242    243    243    243
##   [69,]    215    234    243    240    243    243    243    243    243
##   [70,]    217    243    241    243    243    243    243    243    243
##   [71,]    208    222    231    238    243    243    243    243    243
##   [72,]    194    202    201    214    224    235    243    243    243
##   [73,]    183    185    183    190    202    214    229    232    237
##   [74,]    182    182    182    180    182    195    207    209    213
##   [75,]    170    174    167    169    173    179    190    190    187
##   [76,]    157    157    155    156    161    167    178    184    182
##   [77,]    143    145    143    143    149    155    164    171    158
##   [78,]    130    133    132    130    137    142    149    147    141
##   [79,]    121    123    123    122    125    129    132    128    126
##   [80,]    121    121    121    121    122    121    121    122    121
##   [81,]    139    121    121    121    121    121    121    121    121
##   [82,]    172    151    139    128    121    121    121    121    121
##   [83,]    194    182    182    160    139    121    121    121    121
##         [,857] [,858] [,859] [,860] [,861] [,862] [,863] [,864] [,865]
##    [1,]     29     31     34     37     41     44     48     51     54
##    [2,]     35     36     39     43     46     50     52     55     57
##    [3,]     39     41     45     49     52     55     57     58     60
##    [4,]     41     44     48     53     56     58     59     60     60
##    [5,]     43     46     51     55     57     59     60     60     61
##    [6,]     45     47     51     55     57     59     60     60     62
##    [7,]     47     49     52     55     56     58     59     60     64
##    [8,]     49     50     52     55     56     58     59     60     65
##    [9,]     52     53     54     56     57     58     59     60     62
##   [10,]     54     55     56     57     57     58     59     60     60
##   [11,]     56     56     57     57     58     58     59     59     60
##   [12,]     57     57     57     58     58     58     59     59     59
##   [13,]     59     58     58     59     59     59     59     59     60
##   [14,]     60     60     60     60     60     60     60     60     60
##   [15,]     60     60     60     60     60     60     60     60     60
##   [16,]     60     60     60     60     60     60     60     60     60
##   [17,]     62     60     60     60     60     60     60     60     60
##   [18,]     67     62     60     60     60     60     60     60     60
##   [19,]     69     63     61     60     60     60     60     60     60
##   [20,]     70     63     61     60     60     60     60     60     60
##   [21,]     70     63     60     60     60     60     60     60     60
##   [22,]     67     60     61     60     60     60     60     60     60
##   [23,]     78     72     71     72     73     75     77     80     81
##   [24,]     88     86     87     89     92     97    102    111    111
##   [25,]     99    100    104    106    108    114    121    134    145
##   [26,]    112    110    113    114    116    121    134    149    168
##   [27,]    120    120    121    121    124    137    151    170    180
##   [28,]    121    121    121    121    130    147    168    181    182
##   [29,]    121    121    120    121    126    143    167    173    167
##   [30,]    112    111    115    118    121    121    121    121    121
##   [31,]    100    102    106    110    113    116    118    121    121
##   [32,]     88     93     98    103    107    112    116    121    121
##   [33,]     76     84     90     96    101    107    113    120    121
##   [34,]     64     74     81     87     94    101    108    117    121
##   [35,]     61     64     71     78     86     94    105    116    121
##   [36,]     60     60     60     68     75     86    100    111    114
##   [37,]     60     60     60     60     68     81     96    107    111
##   [38,]     60     60     60     60     64     76     90    102    108
##   [39,]     60     60     60     60     66     74     85     97    105
##   [40,]     60     60     60     60     62     72     84     95    102
##   [41,]     60     60     60     60     67     71     81     91     98
##   [42,]     60     60     60     60     67     72     78     85     92
##   [43,]     60     60     60     60     65     69     72     78     85
##   [44,]     60     60     60     60     62     63     64     70     78
##   [45,]     60     60     60     60     60     60     60     60     72
##   [46,]     60     60     60     60     60     60     60     63     69
##   [47,]     60     60     60     60     60     60     60     60     64
##   [48,]     60     60     60     60     60     60     60     60     60
##   [49,]     60     60     60     60     60     60     60     60     60
##   [50,]     64     60     60     60     60     60     60     60     60
##   [51,]     74     75     70     64     60     60     60     60     60
##   [52,]     88     90     84     76     67     60     60     60     60
##   [53,]    102    105     97     88     79     67     60     60     60
##   [54,]    116    121    111    100     90     76     60     60     60
##   [55,]    122    122    121    112    102     88     74     67     62
##   [56,]    128    130    126    121    113    100     87     80     73
##   [57,]    141    143    138    131    125    113     95     88     80
##   [58,]    162    156    149    143    136    121    108     99     90
##   [59,]    172    165    157    150    144    134    121    110    101
##   [60,]    185    178    169    163    157    151    131    119    111
##   [61,]    200    191    182    179    177    182    161    138    121
##   [62,]    217    207    197    190    186    184    182    158    142
##   [63,]    233    223    213    206    197    188    182    172    159
##   [64,]    243    238    228    221    209    199    192    182    176
##   [65,]    243    243    243    234    222    214    209    196    182
##   [66,]    243    243    243    243    238    235    234    219    214
##   [67,]    243    243    243    243    243    243    243    243    232
##   [68,]    243    243    243    243    243    243    243    243    243
##   [69,]    243    243    243    243    243    243    243    243    243
##   [70,]    243    243    243    243    243    243    243    243    243
##   [71,]    243    243    243    243    243    243    243    243    243
##   [72,]    243    243    243    243    243    243    243    243    243
##   [73,]    243    243    243    240    242    243    243    243    243
##   [74,]    199    182    206    235    242    243    243    243    243
##   [75,]    183    184    182    226    243    243    243    243    243
##   [76,]    177    179    182    208    243    243    243    243    243
##   [77,]    163    166    175    186    206    222    235    243    243
##   [78,]    147    153    167    178    182    201    222    243    243
##   [79,]    138    145    163    177    181    182    209    243    243
##   [80,]    125    133    161    177    181    182    182    197    213
##   [81,]    121    121    161    179    182    182    182    182    208
##   [82,]    121    149    173    182    182    182    182    182    190
##   [83,]    121    143    157    176    182    182    182    184    185
##         [,866] [,867] [,868] [,869] [,870] [,871] [,872] [,873] [,874]
##    [1,]     56     58     60     61     63     65     68     70     74
##    [2,]     58     60     61     62     65     68     72     77     83
##    [3,]     61     61     63     65     69     73     78     85     91
##    [4,]     61     63     66     70     74     79     85     92     99
##    [5,]     63     67     71     76     81     87     93    100    106
##    [6,]     66     71     78     84     89     95    101    108    112
##    [7,]     69     76     84     92     98    104    109    114    117
##    [8,]     73     82     92    101    108    112    115    118    120
##    [9,]     75     90    103    111    116    118    120    121    121
##   [10,]     73     96    107    113    118    120    121    121    121
##   [11,]     63     78     95    106    114    119    121    121    121
##   [12,]     60     60     82     95    107    118    121    121    121
##   [13,]     60     60     72     86    101    119    121    121    121
##   [14,]     60     60     60     73     89    104    117    121    115
##   [15,]     60     60     60     60     75     90     92     83     96
##   [16,]     60     60     60     60     60     68     66     60     74
##   [17,]     60     60     60     60     60     60     60     60     60
##   [18,]     60     60     60     60     60     60     60     60     60
##   [19,]     60     60     60     60     60     60     60     60     60
##   [20,]     60     60     60     60     60     60     60     60     60
##   [21,]     60     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     81     69     60     60     60     60     60     60     60
##   [24,]    111     96     87     73     65     60     60     60     60
##   [25,]    142    121    121    104     89     71     65     60     60
##   [26,]    182    157    135    121    106    102     88     80     69
##   [27,]    179    182    172    150    139    132    113    101     95
##   [28,]    181    182    182    182    182    171    139    121    121
##   [29,]    176    182    182    182    182    182    172    169    147
##   [30,]    144    163    176    182    182    182    182    182    182
##   [31,]    121    147    157    161    172    182    182    172    162
##   [32,]    135    138    142    144    150    154    145    150    150
##   [33,]    125    128    127    129    129    126    123    127    149
##   [34,]    121    121    122    121    122    123    121    159    162
##   [35,]    121    121    121    121    122    121    147    182    182
##   [36,]    118    120    121    121    121    121    129    136    152
##   [37,]    115    119    121    121    121    121    121    121    121
##   [38,]    113    118    121    121    121    121    121    121    121
##   [39,]    111    118    121    121    121    121    121    121    121
##   [40,]    110    118    121    121    121    121    121    133    150
##   [41,]    105    111    116    121    121    121    121    131    148
##   [42,]     99    105    111    115    119    121    121    121    128
##   [43,]     92     99    106    113    119    121    121    121    121
##   [44,]     86     93    101    111    119    121    121    121    121
##   [45,]     81     89     98    112    121    121    121    121    121
##   [46,]     78     88     97    114    121    121    121    121    121
##   [47,]     71     80     89    101    113    119    121    121    121
##   [48,]     60     69     77     90    102    110    121    121    121
##   [49,]     60     60     65     78     88     97    105    116    121
##   [50,]     60     60     60     65     72     81     87     98    109
##   [51,]     60     60     60     60     60     66     67     79     88
##   [52,]     60     60     60     60     60     60     60     60     66
##   [53,]     60     60     60     60     60     60     60     60     60
##   [54,]     60     60     60     60     60     60     60     60     60
##   [55,]     60     60     60     60     60     60     60     60     60
##   [56,]     66     60     60     60     60     60     60     60     60
##   [57,]     72     65     60     60     60     60     60     60     60
##   [58,]     82     74     63     60     60     60     60     60     60
##   [59,]     93     87     79     73     65     60     60     60     60
##   [60,]    105    101     98     90     80     76     72     67     62
##   [61,]    118    117    119    105     93     89     82     76     69
##   [62,]    131    128    124    118    104    101     96     89     81
##   [63,]    155    149    136    121    114    113    110    103     90
##   [64,]    175    166    156    147    134    129    124    117    103
##   [65,]    187    182    177    182    165    153    140    129    116
##   [66,]    204    196    185    186    182    170    157    139    125
##   [67,]    222    215    206    203    191    182    172    152    134
##   [68,]    233    227    220    223    202    185    182    165    151
##   [69,]    243    240    240    243    220    192    180    177    170
##   [70,]    243    243    243    243    243    212    197    182    182
##   [71,]    243    243    243    243    231    222    213    209    206
##   [72,]    243    243    243    243    243    233    230    229    228
##   [73,]    243    243    243    243    243    243    243    243    243
##   [74,]    242    242    242    242    243    243    243    243    243
##   [75,]    242    242    242    242    243    243    243    243    243
##   [76,]    242    242    242    242    242    243    243    243    243
##   [77,]    241    241    242    242    242    243    243    243    243
##   [78,]    238    241    242    242    243    243    243    243    243
##   [79,]    232    240    242    242    243    243    242    243    243
##   [80,]    201    237    243    243    236    237    239    242    243
##   [81,]    243    182    182    206    219    226    234    240    243
##   [82,]    189    187    183    182    203    218    230    239    243
##   [83,]    182    182    182    201    207    220    234    243    247
##         [,875] [,876] [,877] [,878] [,879] [,880] [,881] [,882] [,883]
##    [1,]     77     79     79     79     80     80     81     82     82
##    [2,]     86     88     88     87     87     87     88     89     89
##    [3,]     95     96     96     94     93     94     95     96     96
##    [4,]    102    104    103    101     99     99    100    101    101
##    [5,]    109    110    110    108    105    105    106    106    107
##    [6,]    115    116    116    114    111    110    111    111    112
##    [7,]    119    120    120    119    117    115    116    116    117
##    [8,]    121    121    121    121    120    120    120    120    120
##    [9,]    121    121    121    121    121    121    121    121    121
##   [10,]    121    121    121    121    121    121    121    121    121
##   [11,]    121    121    121    121    121    121    121    121    121
##   [12,]    121    121    121    121    121    121    121    121    121
##   [13,]    121    121    121    121    121    121    121    121    121
##   [14,]    118    121    119    121    121    121    121    121    121
##   [15,]    101    108    114    119    121    121    121    121    117
##   [16,]     81     90     97    108    107    111    112    104    105
##   [17,]     60     71     76     88     91     95     92     89     89
##   [18,]     60     60     60     71     75     77     77     75     72
##   [19,]     60     60     60     60     64     65     65     64     60
##   [20,]     60     60     60     60     60     61     61     60     61
##   [21,]     60     60     60     60     60     60     60     60     60
##   [22,]     60     60     60     60     60     60     60     60     60
##   [23,]     60     60     60     60     60     60     60     60     60
##   [24,]     60     60     60     60     60     60     60     60     60
##   [25,]     60     60     60     60     60     60     60     60     60
##   [26,]     60     60     60     60     60     60     60     60     60
##   [27,]     81     71     66     60     60     60     63     60     60
##   [28,]    106     95     86     80     81     82     74     74     67
##   [29,]    128    115    108    105    111    103     94     92     87
##   [30,]    149    131    121    121    124    121    111    110    107
##   [31,]    154    139    126    142    146    145    138    132    132
##   [32,]    151    146    149    160    170    182    182    165    160
##   [33,]    161    164    169    177    181    181    182    182    182
##   [34,]    182    182    182    180    182    182    182    183    183
##   [35,]    177    182    182    182    181    182    182    184    185
##   [36,]    152    152    160    175    180    182    185    187    187
##   [37,]    121    121    153    170    179    182    192    199    194
##   [38,]    121    130    156    177    187    204    216    228    209
##   [39,]    142    172    182    185    203    219    243    238    235
##   [40,]    172    178    181    192    203    218    236    243    243
##   [41,]    154    177    182    182    194    208    223    243    243
##   [42,]    131    155    176    181    182    189    204    214    223
##   [43,]    121    135    164    178    182    182    182    182    197
##   [44,]    121    134    158    182    182    182    182    181    185
##   [45,]    121    136    147    154    162    166    165    178    182
##   [46,]    121    130    138    135    134    132    121    162    182
##   [47,]    121    122    124    125    124    121    121    141    169
##   [48,]    121    121    121    121    121    116    121    119    127
##   [49,]    121    117    106    108    108     99     98     90     91
##   [50,]    112     92     88     86     77     71     60     62     61
##   [51,]     83     69     71     65     62     60     62     60     61
##   [52,]     67     60     60     61     60     60     60     60     60
##   [53,]     60     61     60     60     60     60     60     60     69
##   [54,]     60     60     60     60     60     60     60     72     90
##   [55,]     60     60     60     60     60     60     81     99    105
##   [56,]     60     60     60     60     60     81    111    120    121
##   [57,]     60     60     60     60     60     60    108    120    121
##   [58,]     60     60     60     60     60     60     87    121    121
##   [59,]     60     60     60     60     60     60     60     90    121
##   [60,]     60     60     60     60     60     60     60     60     95
##   [61,]     60     60     60     60     60     60     60     72     87
##   [62,]     69     60     60     60     60     60     60     60     69
##   [63,]     76     68     60     60     60     60     60     60     60
##   [64,]     88     78     69     60     60     60     60     60     60
##   [65,]    100     89     80     71     60     60     60     60     60
##   [66,]    108     97     90     82     72     60     60     60     60
##   [67,]    118    109    105    101     90     78     63     60     60
##   [68,]    136    121    121    121    109     96     74     60     60
##   [69,]    164    162    167    147    127    114     86     66     60
##   [70,]    182    182    179    182    145    113     89     80     71
##   [71,]    197    189    185    182    158    115     99     93     86
##   [72,]    217    207    195    185    182    118    110    106    104
##   [73,]    237    221    203    185    177    145    120    119    119
##   [74,]    243    243    217    201    182    163    154    152    158
##   [75,]    243    243    237    221    206    185    178    188    182
##   [76,]    243    243    243    243    228    210    209    209    196
##   [77,]    243    243    243    243    243    226    227    227    215
##   [78,]    243    243    244    244    244    244    244    243    237
##   [79,]    244    244    245    246    246    247    245    245    243
##   [80,]    244    245    247    249    251    250    249    248    245
##   [81,]    245    247    250    252    255    254    255    254    250
##   [82,]    247    250    253    256    261    262    267    270    263
##   [83,]    250    253    256    259    270    282    292    304    285
##         [,884] [,885] [,886] [,887] [,888] [,889] [,890] [,891] [,892]
##    [1,]     82     81     80     78     76     74     71     68     64
##    [2,]     89     89     88     86     85     83     81     76     71
##    [3,]     96     97     96     94     94     93     91     83     78
##    [4,]    102    103    103    103    104    103    102     96     89
##    [5,]    107    109    110    111    112    112    111    107    101
##    [6,]    113    114    116    117    118    118    118    115    112
##    [7,]    117    118    119    120    121    121    121    121    120
##    [8,]    119    119    120    121    121    121    122    122    122
##    [9,]    121    121    121    121    121    122    123    123    123
##   [10,]    121    121    121    121    121    123    124    124    125
##   [11,]    121    121    121    121    121    123    124    125    126
##   [12,]    121    121    121    121    121    123    125    126    127
##   [13,]    121    121    121    121    121    121    122    123    121
##   [14,]    121    121    121    121    121    121    121    121    121
##   [15,]    121    120    121    121    121    121    121    121    121
##   [16,]    103    110    117    118    119    120    121    121    121
##   [17,]     85     95    106    111    116    120    121    121    121
##   [18,]     67     82     97    105    112    121    121    121    121
##   [19,]     61     76     87     96    103    110    121    121    121
##   [20,]     61     70     78     85     90     94    104    113    114
##   [21,]     60     66     70     73     75     74     85     94    100
##   [22,]     60     60     63     64     64     60     73     83     92
##   [23,]     60     60     60     61     60     61     60     69     80
##   [24,]     60     60     60     60     60     60     60     60     68
##   [25,]     60     60     60     60     60     60     60     60     60
##   [26,]     60     60     60     60     60     60     60     60     60
##   [27,]     60     60     60     60     60     60     60     60     60
##   [28,]     60     60     60     60     60     60     60     60     60
##   [29,]     80     69     67     68     68     68     65     60     60
##   [30,]    101     91     89     90     91     91     82     70     60
##   [31,]    117    110    109    113    114    114    100     88     82
##   [32,]    145    121    121    138    141    130    116    108     99
##   [33,]    182    158    158    158    161    149    129    121    111
##   [34,]    183    182    182    182    182    174    163    141    128
##   [35,]    183    182    182    182    182    182    182    167    151
##   [36,]    183    182    182    182    182    182    182    182    175
##   [37,]    184    182    182    182    182    182    182    182    182
##   [38,]    188    183    182    180    182    182    174    179    182
##   [39,]    202    186    182    168    151    155    158    164    167
##   [40,]    211    189    177    156    121    132    141    146    148
##   [41,]    214    198    187    182    121    121    125    128    130
##   [42,]    210    197    182    152    121    121    121    123    124
##   [43,]    198    192    182    151    121    117    121    121    121
##   [44,]    189    188    182    151    121    111    121    121    121
##   [45,]    183    183    169    147    121     83     94    112    121
##   [46,]    182    155    142    132    121     64     60     81     89
##   [47,]    182    119     86     91     67     65     62     61     67
##   [48,]    121     60     71     62     61     62     61     60     61
##   [49,]     66     69     63     62     61     61     60     79     87
##   [50,]     60     65     61     60     60     60    109    133    148
##   [51,]     61     60     72     88     98    105    162    177    184
##   [52,]     60     86    101    121    121    153    182    182    187
##   [53,]     86     99    115    119    146    167    172    182    194
##   [54,]     97    104    113    121    161    182    182    182    186
##   [55,]    108    110    114    121    141    164    182    182    182
##   [56,]    121    119    119    120    125    144    154    169    169
##   [57,]    121    121    121    121    121    121    121    138    137
##   [58,]    121    121    121    121    121    121    121    121    121
##   [59,]    121    121    121    121    121    121    121    121    121
##   [60,]    121    121    121    121    121    121    121    129    135
##   [61,]    121    121    121    121    121    121    139    152    167
##   [62,]     75    100    114    120    130    147    158    175    181
##   [63,]     60     60     97    121    166    172    173    182    182
##   [64,]     60     60     91    133    161    182    182    181    182
##   [65,]     60     77     90    128    144    158    173    182    182
##   [66,]     60     71     87    113    121    137    144    156    165
##   [67,]     60     60     67    106    119    121    121    130    141
##   [68,]     60     60     60    106    118    120    121    121    121
##   [69,]     60     60     60    110    119    121    121    121    121
##   [70,]     60     71    108    116    121    121    121    121    121
##   [71,]     90     89    114    120    121    121    121    121    121
##   [72,]    108    109    119    121    121    121    121    121    121
##   [73,]    130    125    121    121    121    121    121    121    121
##   [74,]    158    145    130    121    121    121    121    121    121
##   [75,]    182    160    140    121    121    121    121    121    121
##   [76,]    189    182    163    131    121    121    121    121    121
##   [77,]    202    192    173    139    121    121    121    121    121
##   [78,]    219    204    187    159    131    121    121    121    121
##   [79,]    232    217    196    182    150    121    121    121    121
##   [80,]    240    226    204    182    165    148    130    121    121
##   [81,]    243    236    213    194    182    167    151    134    121
##   [82,]    254    243    225    206    195    186    173    149    129
##   [83,]    270    255    237    218    206    195    182    170    145
##         [,893] [,894] [,895] [,896] [,897] [,898] [,899] [,900] [,901]
##    [1,]     61     59     58     58     57     57     56     56     56
##    [2,]     68     66     64     62     60     58     56     54     54
##    [3,]     76     74     72     67     63     60     57     54     53
##    [4,]     86     84     79     76     70     66     61     59     57
##    [5,]     98     96     92     86     80     74     70     67     65
##    [6,]    108    107    105    101     94     87     81     78     75
##    [7,]    117    116    115    112    107    100     94     90     87
##    [8,]    122    122    123    121    118    113    108    104    101
##    [9,]    125    125    126    128    128    127    122    118    116
##   [10,]    127    128    131    135    139    141    142    138    136
##   [11,]    129    132    137    143    150    156    161    160    158
##   [12,]    129    136    145    154    162    173    181    182    182
##   [13,]    121    131    150    164    174    181    182    181    182
##   [14,]    121    134    158    177    181    181    181    182    182
##   [15,]    141    153    182    178    181    181    182    182    164
##   [16,]    138    153    162    175    181    182    164    150    133
##   [17,]    133    142    149    157    157    150    121    121    128
##   [18,]    124    129    133    136    134    125    124    123    122
##   [19,]    121    121    122    123    124    123    122    121    122
##   [20,]    119    121    121    121    122    122    121    121    121
##   [21,]    108    111    113    117    121    120    120    121    121
##   [22,]    100    104    105    110    113    115    117    120    121
##   [23,]     89     93     94     99    105    111    115    119    121
##   [24,]     79     82     83     88     97    106    113    121    121
##   [25,]     69     71     72     78     86     97    104    111    118
##   [26,]     60     60     60     67     74     88     94    101    108
##   [27,]     60     60     60     60     64     79     85     91     98
##   [28,]     60     60     60     60     60     71     74     81     87
##   [29,]     60     60     60     60     60     63     64     71     77
##   [30,]     60     60     60     60     60     60     60     60     67
##   [31,]     73     60     60     60     60     60     60     60     60
##   [32,]     90     81     79     72     62     60     60     60     60
##   [33,]    101     98     97     89     77     66     60     60     60
##   [34,]    116    115    115    100     89     83     75     66     60
##   [35,]    146    138    129    116    103     99     94     84     72
##   [36,]    173    162    150    133    117    116    114    103     90
##   [37,]    182    182    170    152    130    124    122    121    109
##   [38,]    182    182    182    154    134    128    124    121    118
##   [39,]    174    182    164    143    132    128    125    123    121
##   [40,]    152    146    145    138    125    124    124    123    121
##   [41,]    128    121    128    124    123    121    121    122    122
##   [42,]    121    123    121    122    121    122    121    121    121
##   [43,]    122    120    121    121    121    121    121    121    121
##   [44,]    121    117    118    119    120    120    121    121    121
##   [45,]    113    111    115    117    119    120    120    120    121
##   [46,]     94    100    114    117    118    119    120    120    121
##   [47,]     73     93    113    117    118    119    120    120    121
##   [48,]     60     91    114    118    119    120    120    121    121
##   [49,]    110    132    147    132    126    121    121    121    121
##   [50,]    159    182    181    164    147    131    121    121    143
##   [51,]    190    204    209    191    173    153    140    154    157
##   [52,]    207    228    243    222    197    182    176    182    175
##   [53,]    212    243    241    243    211    197    182    187    187
##   [54,]    200    216    238    233    222    219    220    214    216
##   [55,]    182    197    205    226    230    243    243    243    240
##   [56,]    172    179    184    191    222    241    243    248    256
##   [57,]    151    166    181    199    211    227    243    255    288
##   [58,]    131    153    182    192    205    219    232    241    255
##   [59,]    121    131    167    182    192    210    228    239    252
##   [60,]    142    137    156    174    182    208    238    242    246
##   [61,]    182    177    172    182    189    198    217    243    240
##   [62,]    180    182    182    180    182    182    201    215    238
##   [63,]    181    182    182    182    182    181    182    191    214
##   [64,]    182    182    182    182    182    180    178    179    192
##   [65,]    182    182    182    182    182    177    173    172    181
##   [66,]    174    179    182    182    173    168    160    159    182
##   [67,]    147    154    164    162    159    148    129    129    153
##   [68,]    121    134    148    158    160    153    121    122    121
##   [69,]    121    121    130    177    182    182    167    128    122
##   [70,]    121    121    121    121    182    182    182    153    121
##   [71,]    121    121    121    121    131    165    182    165    121
##   [72,]    121    121    121    121    121    121    182    151    121
##   [73,]    121    121    121    121    121    121    121    140    121
##   [74,]    121    121    121    121    121    121    121    123    123
##   [75,]    121    121    121    121    121    121    121    121    121
##   [76,]    121    121    121    121    121    121    121    121    121
##   [77,]    121    121    121    121    121    121    121    121    121
##   [78,]    121    121    121    121    121    121    121    121    121
##   [79,]    121    121    121    121    121    121    121    121    121
##   [80,]    121    121    121    121    121    121    121    121    121
##   [81,]    121    121    121    121    121    121    121    121    121
##   [82,]    121    121    121    121    121    121    121    121    121
##   [83,]    121    121    121    121    121    121    121    121    121
##         [,902] [,903] [,904] [,905] [,906] [,907] [,908] [,909] [,910]
##    [1,]     56     57     58     60     62     66     70     75     81
##    [2,]     54     55     57     60     63     66     71     76     81
##    [3,]     54     55     57     60     63     67     72     76     81
##    [4,]     57     57     58     60     62     65     68     72     76
##    [5,]     63     62     62     62     62     63     65     67     72
##    [6,]     73     70     69     66     65     65     66     67     72
##    [7,]     85     82     79     75     74     73     73     73     79
##    [8,]     99     95     92     87     85     84     83     82     88
##    [9,]    114    109    105    100     98     96     95     92     95
##   [10,]    134    128    120    119    117    113    110    105    105
##   [11,]    154    146    134    142    136    129    123    115    115
##   [12,]    176    169    163    166    155    143    133    121    121
##   [13,]    182    182    180    181    182    166    151    136    121
##   [14,]    182    182    182    182    182    182    175    159    154
##   [15,]    166    171    178    182    182    182    182    182    171
##   [16,]    143    155    173    182    182    182    182    182    182
##   [17,]    121    143    168    182    182    182    182    182    182
##   [18,]    121    135    162    181    178    182    182    182    182
##   [19,]    121    121    139    142    160    170    182    182    182
##   [20,]    121    121    121    121    138    154    171    182    181
##   [21,]    121    121    121    121    121    129    157    170    179
##   [22,]    121    121    121    121    121    121    150    173    182
##   [23,]    121    121    121    121    136    170    172    178    181
##   [24,]    121    121    121    121    147    163    182    182    181
##   [25,]    121    121    121    121    140    151    161    174    171
##   [26,]    114    121    121    121    130    136    142    149    129
##   [27,]    103    107    116    121    121    123    125    125    122
##   [28,]     92     99    109    115    121    120    121    121    121
##   [29,]     81     89     99    106    109    116    117    120    121
##   [30,]     69     78     89     97    102    109    114    119    121
##   [31,]     60     72     83     91     97    103    110    118    121
##   [32,]     60     64     73     81     88     94    103    115    119
##   [33,]     60     60     60     69     73     76     86     97    105
##   [34,]     60     60     60     60     60     60     67     79     87
##   [35,]     60     60     60     60     60     60     60     65     73
##   [36,]     79     67     62     60     60     60     60     60     60
##   [37,]     91     76     68     66     63     60     60     60     60
##   [38,]     99     83     75     73     70     69     66     64     63
##   [39,]    106     88     81     80     77     76     74     72     72
##   [40,]    108     92     85     84     82     81     79     78     78
##   [41,]    111     97     92     91     89     89     87     87     88
##   [42,]    105    101     99     98     96     96     95     96     97
##   [43,]    110    107    105    105    104    104    103    104    106
##   [44,]    116    113    112    112    111    112    111    111    112
##   [45,]    120    119    118    119    118    119    117    117    117
##   [46,]    121    121    121    123    121    124    121    121    121
##   [47,]    121    121    127    131    136    135    134    128    130
##   [48,]    122    121    138    142    147    148    147    143    138
##   [49,]    134    142    149    154    158    162    162    153    146
##   [50,]    148    155    160    166    170    176    177    162    152
##   [51,]    160    164    168    173    177    182    181    168    157
##   [52,]    176    178    179    187    187    184    183    174    163
##   [53,]    195    195    200    203    198    194    185    177    168
##   [54,]    214    215    218    224    218    208    193    182    174
##   [55,]    234    234    236    243    243    230    210    194    182
##   [56,]    253    243    243    246    244    243    227    212    200
##   [57,]    304    304    284    255    247    244    243    231    219
##   [58,]    293    304    288    266    248    244    243    243    237
##   [59,]    270    272    272    253    243    243    243    243    243
##   [60,]    261    256    252    246    245    238    235    233    238
##   [61,]    243    248    248    246    243    229    213    203    212
##   [62,]    243    243    245    245    243    221    196    182    191
##   [63,]    238    243    243    243    243    222    182    181    180
##   [64,]    222    243    243    243    243    214    182    171    166
##   [65,]    201    215    226    227    215    202    182    158    143
##   [66,]    182    186    182    191    182    187    150    142    121
##   [67,]    169    169    167    161    143    146    124    122    123
##   [68,]    138    137    134    121    127    123    121    122    121
##   [69,]    121    125    124    122    121    121    121    121    121
##   [70,]    121    121    121    121    121    121    121    121    121
##   [71,]    121    121    121    121    121    121    121    121    121
##   [72,]    121    121    121    121    121    121    121    121    121
##   [73,]    121    121    121    121    121    121    121    121    162
##   [74,]    122    121    121    121    121    131    145    172    180
##   [75,]    123    122    121    121    123    139    157    168    182
##   [76,]    121    121    121    121    124    137    151    166    182
##   [77,]    121    121    121    121    121    131    145    159    169
##   [78,]    121    121    121    121    121    121    136    147    155
##   [79,]    121    121    121    121    121    121    128    134    138
##   [80,]    121    121    121    121    121    121    121    123    124
##   [81,]    121    121    121    121    121    121    121    121    121
##   [82,]    121    121    121    121    121    121    121    121    121
##   [83,]    121    121    121    121    121    121    121    121    121
##         [,911] [,912] [,913] [,914] [,915] [,916] [,917] [,918] [,919]
##    [1,]     87     94    100    105    110    114    118    123    129
##    [2,]     87     94    100    106    111    115    119    124    131
##    [3,]     87     95    102    109    114    118    121    126    135
##    [4,]     84     94    103    110    115    118    121    127    137
##    [5,]     82     93    104    112    117    120    121    129    143
##    [6,]     84     96    107    115    119    121    121    124    134
##    [7,]     91    103    112    117    120    121    121    121    126
##    [8,]     98    108    115    119    121    121    121    121    122
##    [9,]    103    112    118    121    121    121    121    121    121
##   [10,]    110    116    120    121    121    121    121    121    121
##   [11,]    118    120    121    121    121    121    121    121    121
##   [12,]    122    123    121    121    121    121    121    121    121
##   [13,]    133    129    125    121    121    121    121    121    121
##   [14,]    145    138    133    126    121    121    121    121    121
##   [15,]    158    149    143    133    121    121    121    121    121
##   [16,]    174    172    170    151    130    121    133    150    139
##   [17,]    182    181    182    182    156    160    159    182    166
##   [18,]    182    182    182    182    170    170    178    182    182
##   [19,]    182    182    182    182    182    180    180    182    182
##   [20,]    182    182    182    182    182    182    182    182    182
##   [21,]    182    182    182    182    182    182    182    182    182
##   [22,]    182    182    182    182    182    182    182    182    182
##   [23,]    181    182    182    182    182    182    182    182    182
##   [24,]    176    179    182    182    182    182    182    182    182
##   [25,]    165    173    182    182    182    182    182    182    182
##   [26,]    147    160    171    182    182    182    182    182    182
##   [27,]    126    144    154    162    170    173    170    155    164
##   [28,]    121    130    136    139    140    145    138    121    138
##   [29,]    121    121    124    121    121    129    126    126    121
##   [30,]    121    121    121    121    121    121    122    121    122
##   [31,]    121    121    121    121    121    120    120    121    121
##   [32,]    119    121    121    121    121    120    118    119    119
##   [33,]    113    121    121    121    121    119    116    117    118
##   [34,]     98    106    115    121    117    113    114    115    117
##   [35,]     81     87     94     92    106    109    112    114    116
##   [36,]     66     67     69     68     97    107    111    113    115
##   [37,]     60     60     60     68     95    105    110    112    114
##   [38,]     62     60     60     76     96    104    109    111    114
##   [39,]     70     69     72     92     98    102    108    111    113
##   [40,]     77     77     80     92     96    104    110    112    114
##   [41,]     87     88     92     95    101    110    118    117    119
##   [42,]     98    100    103    106    113    121    122    121    131
##   [43,]    107    108    110    113    119    128    133    141    150
##   [44,]    113    114    116    118    120    135    146    157    170
##   [45,]    118    120    120    121    124    138    151    164    177
##   [46,]    121    121    121    122    127    142    150    161    168
##   [47,]    128    126    125    123    126    138    146    154    161
##   [48,]    134    130    127    124    124    132    139    146    153
##   [49,]    139    134    128    124    122    127    133    141    148
##   [50,]    144    136    128    121    121    121    124    132    139
##   [51,]    147    138    129    121    121    121    121    125    132
##   [52,]    152    142    132    121    121    121    121    121    127
##   [53,]    158    147    137    128    121    121    121    121    121
##   [54,]    164    154    143    128    121    121    121    121    121
##   [55,]    173    162    150    129    121    121    121    121    121
##   [56,]    188    177    164    141    121    121    121    121    121
##   [57,]    205    192    182    152    121    121    121    121    121
##   [58,]    221    204    184    162    121    121    121    121    121
##   [59,]    243    224    198    166    131    121    122    121    121
##   [60,]    243    243    204    167    121    126    122    122    121
##   [61,]    211    211    200    166    121    121    122    122    122
##   [62,]    193    182    182    151    121    121    121    121    122
##   [63,]    184    173    154    130    123    122    122    121    121
##   [64,]    155    150    135    123    122    121    122    121    121
##   [65,]    130    127    122    123    122    122    121    121    152
##   [66,]    125    122    121    122    122    121    121    182    170
##   [67,]    122    121    121    121    121    121    128    151    182
##   [68,]    121    121    121    121    121    121    121    151    182
##   [69,]    121    121    121    121    121    121    125    129    162
##   [70,]    121    121    121    121    121    121    142    121    162
##   [71,]    121    121    121    139    145    162    182    182    182
##   [72,]    121    152    164    170    175    191    199    205    205
##   [73,]    182    167    182    188    199    217    226    231    243
##   [74,]    180    181    181    195    207    228    243    243    242
##   [75,]    181    182    182    182    185    182    213    243    243
##   [76,]    182    182    181    182    182    183    182    209    233
##   [77,]    182    169    172    178    181    182    191    195    227
##   [78,]    154    154    158    168    176    182    182    184    184
##   [79,]    138    140    142    156    169    182    182    182    182
##   [80,]    124    122    121    132    151    176    182    182    182
##   [81,]    121    121    121    121    121    169    182    182    182
##   [82,]    121    121    121    121    162    182    179    182    182
##   [83,]    121    121    121    146    170    179    172    169    170
##         [,920] [,921] [,922] [,923] [,924] [,925] [,926] [,927] [,928]
##    [1,]    137    145    152    159    163    168    173    177    179
##    [2,]    139    148    158    167    172    177    180    184    186
##    [3,]    145    156    167    173    182    188    190    190    192
##    [4,]    149    161    170    176    181    184    186    187    188
##    [5,]    156    167    172    175    177    180    182    183    184
##    [6,]    148    160    165    167    169    172    176    179    182
##    [7,]    135    146    154    156    159    163    168    174    178
##    [8,]    127    134    140    142    146    151    159    167    174
##    [9,]    121    123    126    128    131    138    148    159    170
##   [10,]    121    121    121    122    123    129    139    149    160
##   [11,]    121    121    121    121    121    125    133    141    150
##   [12,]    121    121    121    121    121    124    129    133    141
##   [13,]    121    121    121    121    121    121    121    121    130
##   [14,]    121    121    121    121    121    121    121    121    121
##   [15,]    121    121    121    121    121    121    121    121    121
##   [16,]    132    127    121    121    121    121    121    121    121
##   [17,]    160    157    152    135    125    121    121    121    121
##   [18,]    177    182    168    151    131    122    121    121    121
##   [19,]    182    181    182    160    132    122    121    121    121
##   [20,]    182    182    182    160    132    121    121    121    121
##   [21,]    182    182    182    155    125    122    122    121    121
##   [22,]    182    182    182    154    128    121    121    121    121
##   [23,]    182    182    182    153    125    122    122    122    121
##   [24,]    182    178    159    143    126    123    122    122    121
##   [25,]    182    172    155    125    122    122    122    122    122
##   [26,]    182    182    164    134    122    121    122    122    121
##   [27,]    182    182    182    149    121    121    122    122    121
##   [28,]    161    169    170    153    124    122    122    122    121
##   [29,]    137    136    133    121    125    122    122    122    121
##   [30,]    121    124    121    122    121    122    122    122    121
##   [31,]    121    121    121    121    121    121    121    121    121
##   [32,]    120    121    121    121    121    121    121    121    121
##   [33,]    119    120    120    120    121    121    121    121    121
##   [34,]    118    119    119    120    120    121    121    121    121
##   [35,]    118    118    119    119    120    121    121    121    121
##   [36,]    117    118    118    119    120    120    121    121    121
##   [37,]    116    117    118    119    120    120    121    121    121
##   [38,]    116    117    118    119    120    120    121    121    121
##   [39,]    115    117    118    120    120    121    121    121    121
##   [40,]    116    118    120    121    121    121    121    121    121
##   [41,]    120    120    121    121    121    124    121    121    121
##   [42,]    136    138    127    121    121    136    134    121    149
##   [43,]    158    163    167    142    149    160    169    163    166
##   [44,]    182    182    181    182    176    182    180    182    182
##   [45,]    181    182    182    182    182    186    192    196    199
##   [46,]    175    182    182    182    186    195    203    211    221
##   [47,]    168    174    181    182    191    202    214    223    238
##   [48,]    160    166    174    182    191    205    222    238    242
##   [49,]    154    164    173    178    182    198    220    243    243
##   [50,]    147    156    166    172    178    182    205    219    236
##   [51,]    140    150    160    167    174    182    192    198    214
##   [52,]    133    143    153    160    167    173    178    181    192
##   [53,]    126    135    145    152    159    166    169    174    179
##   [54,]    121    127    136    144    151    158    162    167    174
##   [55,]    121    121    127    136    143    150    155    161    168
##   [56,]    121    121    121    128    135    142    149    157    166
##   [57,]    121    121    121    121    127    135    143    153    163
##   [58,]    121    121    121    121    121    131    139    150    161
##   [59,]    121    121    121    121    123    128    134    146    158
##   [60,]    122    122    121    121    121    127    129    142    154
##   [61,]    123    122    122    121    121    121    123    136    148
##   [62,]    124    122    122    121    121    121    121    130    140
##   [63,]    127    122    122    121    121    121    121    123    132
##   [64,]    131    121    121    121    121    121    121    121    121
##   [65,]    183    192    187    167    162    152    131    121    121
##   [66,]    200    221    209    206    199    190    182    146    121
##   [67,]    220    240    235    234    223    211    199    180    171
##   [68,]    223    243    242    245    243    231    214    202    190
##   [69,]    198    243    243    247    248    243    228    217    205
##   [70,]    192    243    243    254    260    259    250    237    225
##   [71,]    179    223    243    263    277    284    270    252    243
##   [72,]    209    233    253    278    297    302    288    265    255
##   [73,]    243    259    284    304    296    303    297    277    265
##   [74,]    259    275    295    302    303    303    302    288    274
##   [75,]    252    268    281    292    304    304    304    304    287
##   [76,]    243    255    265    280    296    304    304    304    298
##   [77,]    242    243    243    259    275    292    304    304    304
##   [78,]    213    225    233    240    252    276    299    304    304
##   [79,]    183    182    211    230    243    255    267    284    304
##   [80,]    182    194    200    219    243    243    243    243    243
##   [81,]    182    186    189    192    199    225    234    240    243
##   [82,]    180    181    182    182    182    195    226    239    243
##   [83,]    176    181    182    182    182    199    217    234    243
##         [,929] [,930] [,931] [,932] [,933] [,934] [,935] [,936] [,937]
##    [1,]    179    179    179    180    182    186    189    187    180
##    [2,]    186    188    187    186    189    193    195    192    185
##    [3,]    194    194    192    191    194    198    199    196    189
##    [4,]    190    192    192    192    194    197    197    194    186
##    [5,]    186    188    189    192    195    196    194    191    187
##    [6,]    183    185    188    195    201    201    196    191    188
##    [7,]    181    185    193    201    210    207    200    193    189
##    [8,]    179    188    201    214    222    215    205    196    190
##    [9,]    175    188    214    230    236    229    210    196    188
##   [10,]    168    179    205    225    235    232    208    194    187
##   [11,]    160    174    191    217    229    220    208    195    187
##   [12,]    150    160    173    191    205    204    200    182    186
##   [13,]    138    148    161    174    182    188    188    182    182
##   [14,]    126    135    149    163    173    182    184    184    182
##   [15,]    121    121    136    151    161    171    182    182    181
##   [16,]    121    121    126    142    152    160    169    182    175
##   [17,]    121    121    121    126    137    141    147    145    158
##   [18,]    121    121    121    121    121    121    121    121    140
##   [19,]    121    121    121    121    121    121    121    121    127
##   [20,]    121    121    121    121    121    121    121    121    124
##   [21,]    121    121    121    121    121    121    121    121    121
##   [22,]    121    121    121    121    121    121    121    121    121
##   [23,]    121    121    121    121    121    121    121    121    121
##   [24,]    121    121    121    121    121    121    121    121    121
##   [25,]    121    121    121    121    121    121    121    121    121
##   [26,]    121    121    121    121    121    121    121    121    121
##   [27,]    121    121    121    121    121    121    121    121    121
##   [28,]    121    121    121    121    121    121    121    121    121
##   [29,]    121    121    121    121    121    121    121    121    121
##   [30,]    121    121    121    121    121    121    121    121    121
##   [31,]    121    121    121    121    121    121    121    121    121
##   [32,]    121    121    121    121    121    121    121    121    121
##   [33,]    121    121    121    121    121    121    121    121    121
##   [34,]    121    121    121    121    121    121    121    121    121
##   [35,]    121    121    121    121    121    121    121    121    121
##   [36,]    121    121    121    121    121    121    121    121    121
##   [37,]    121    121    121    121    121    121    121    121    121
##   [38,]    121    121    121    121    121    121    121    121    121
##   [39,]    122    122    121    121    121    121    121    121    121
##   [40,]    125    124    121    121    121    121    121    121    121
##   [41,]    132    130    126    123    121    121    121    121    121
##   [42,]    140    137    133    128    121    121    121    121    121
##   [43,]    165    151    145    140    129    121    135    133    121
##   [44,]    182    171    164    164    158    161    163    182    163
##   [45,]    192    186    180    187    188    188    188    188    185
##   [46,]    216    205    206    204    204    203    204    205    201
##   [47,]    230    218    218    219    216    214    214    215    214
##   [48,]    243    237    237    237    232    230    229    231    236
##   [49,]    243    243    243    243    243    241    239    243    241
##   [50,]    243    243    243    243    242    242    242    243    243
##   [51,]    233    243    243    237    240    242    243    243    243
##   [52,]    212    228    226    230    234    241    243    243    243
##   [53,]    182    200    210    220    231    242    243    243    243
##   [54,]    181    186    191    207    224    243    243    243    243
##   [55,]    176    179    182    182    202    236    243    243    243
##   [56,]    172    177    181    182    194    227    241    243    243
##   [57,]    170    176    182    184    202    233    243    250    265
##   [58,]    168    175    182    186    202    225    243    255    275
##   [59,]    166    174    182    189    199    218    235    243    266
##   [60,]    163    172    182    188    196    212    231    243    253
##   [61,]    156    165    172    179    186    205    228    241    249
##   [62,]    149    157    165    172    178    194    224    243    250
##   [63,]    140    149    159    167    179    194    213    227    239
##   [64,]    132    143    153    163    175    182    202    217    229
##   [65,]    124    140    151    161    173    182    195    210    224
##   [66,]    141    144    155    163    177    186    197    211    225
##   [67,]    162    162    164    168    176    182    200    216    232
##   [68,]    182    178    175    175    178    182    197    219    243
##   [69,]    193    182    182    180    180    181    182    213    228
##   [70,]    212    208    197    191    184    182    182    204    222
##   [71,]    231    229    218    215    202    182    202    208    222
##   [72,]    247    243    237    236    227    219    220    227    237
##   [73,]    254    245    244    243    243    237    238    243    241
##   [74,]    257    243    243    243    243    243    243    243    243
##   [75,]    263    243    243    243    243    243    243    243    243
##   [76,]    272    243    243    243    243    243    243    243    243
##   [77,]    280    243    243    243    243    243    243    243    243
##   [78,]    293    267    243    243    241    243    243    243    243
##   [79,]    277    261    254    243    231    228    237    243    243
##   [80,]    269    260    251    243    216    203    215    226    238
##   [81,]    243    247    248    245    192    186    190    206    220
##   [82,]    243    243    243    244    243    182    185    182    198
##   [83,]    243    243    243    243    243    196    182    183    182
##         [,938] [,939] [,940] [,941] [,942] [,943] [,944] [,945] [,946]
##    [1,]    170    158    147    138    131    130    132    137    140
##    [2,]    173    159    147    139    134    134    140    146    150
##    [3,]    172    156    144    141    137    143    151    156    159
##    [4,]    173    158    150    154    158    158    163    167    164
##    [5,]    180    174    167    173    179    176    176    175    169
##    [6,]    185    182    187    193    201    193    188    181    171
##    [7,]    189    192    202    214    218    211    200    187    173
##    [8,]    191    200    213    221    226    218    207    192    175
##    [9,]    191    197    204    214    228    223    205    186    171
##   [10,]    187    190    194    203    209    200    187    174    161
##   [11,]    184    184    187    195    212    199    186    175    163
##   [12,]    183    182    182    197    226    210    187    179    177
##   [13,]    182    182    182    182    243    243    211    203    192
##   [14,]    181    182    182    182    243    243    227    224    210
##   [15,]    180    182    182    206    232    243    242    243    235
##   [16,]    178    182    182    194    210    225    243    243    234
##   [17,]    167    174    179    182    190    204    215    232    240
##   [18,]    156    164    172    182    182    182    185    204    222
##   [19,]    144    152    159    167    176    179    180    182    193
##   [20,]    134    140    143    153    160    167    174    179    181
##   [21,]    125    126    127    137    149    161    171    178    181
##   [22,]    121    121    121    121    139    158    173    179    182
##   [23,]    121    121    121    128    140    162    176    182    197
##   [24,]    121    121    125    138    151    173    181    182    187
##   [25,]    121    121    128    139    152    174    182    180    182
##   [26,]    121    121    129    138    149    168    176    178    181
##   [27,]    121    121    121    130    140    156    165    174    182
##   [28,]    121    121    121    121    126    145    151    158    164
##   [29,]    121    121    121    121    127    132    135    143    152
##   [30,]    121    121    121    121    121    123    122    127    139
##   [31,]    121    121    121    121    121    121    121    121    129
##   [32,]    121    121    121    121    121    121    121    124    124
##   [33,]    121    121    121    121    121    121    121    121    121
##   [34,]    121    121    121    121    121    121    121    121    121
##   [35,]    121    121    121    121    121    121    121    121    121
##   [36,]    121    121    121    121    121    121    121    121    121
##   [37,]    121    121    121    121    121    121    121    121    121
##   [38,]    121    121    121    121    121    121    121    121    121
##   [39,]    121    121    121    121    121    121    121    121    121
##   [40,]    121    121    121    121    121    121    121    121    121
##   [41,]    121    121    121    121    121    121    121    121    121
##   [42,]    121    121    129    121    126    121    121    121    121
##   [43,]    131    145    156    171    158    131    121    121    121
##   [44,]    155    165    182    181    183    161    148    121    131
##   [45,]    178    176    182    186    183    182    182    182    152
##   [46,]    192    182    188    188    184    183    182    182    182
##   [47,]    205    201    198    192    185    183    182    182    182
##   [48,]    224    214    207    194    184    183    182    182    182
##   [49,]    243    229    221    194    184    182    182    182    182
##   [50,]    243    243    243    223    189    182    182    182    182
##   [51,]    243    243    243    243    202    182    182    182    182
##   [52,]    243    243    243    236    192    186    182    182    182
##   [53,]    243    243    243    231    204    182    198    195    188
##   [54,]    247    249    247    236    220    221    219    214    208
##   [55,]    256    265    267    251    243    243    243    232    227
##   [56,]    264    277    284    279    274    264    252    243    240
##   [57,]    282    297    303    304    304    295    280    265    248
##   [58,]    304    299    304    304    304    304    304    289    256
##   [59,]    284    291    291    284    274    274    289    278    253
##   [60,]    274    267    261    243    248    244    243    243    243
##   [61,]    265    260    252    245    243    244    240    233    230
##   [62,]    258    253    249    247    246    243    235    223    206
##   [63,]    247    247    248    249    249    246    244    235    210
##   [64,]    238    243    248    253    252    249    246    243    215
##   [65,]    235    243    256    268    263    255    247    243    226
##   [66,]    236    243    278    304    283    264    248    243    237
##   [67,]    243    261    290    299    304    270    243    243    243
##   [68,]    249    263    293    304    304    287    286    282    289
##   [69,]    243    259    293    304    304    304    304    304    303
##   [70,]    235    258    286    299    304    304    304    304    304
##   [71,]    235    255    277    285    289    297    304    304    304
##   [72,]    242    257    267    273    275    278    285    294    302
##   [73,]    243    250    256    258    259    258    261    270    285
##   [74,]    243    243    246    246    246    244    243    250    266
##   [75,]    243    243    243    243    243    242    242    242    249
##   [76,]    243    243    243    243    243    242    240    240    243
##   [77,]    243    243    243    243    243    241    238    232    234
##   [78,]    243    243    243    243    243    240    235    223    222
##   [79,]    243    243    243    243    243    237    228    205    207
##   [80,]    243    243    243    243    243    243    227    194    182
##   [81,]    238    243    243    243    243    243    243    197    182
##   [82,]    221    243    243    243    243    243    243    203    182
##   [83,]    199    224    238    243    243    243    243    213    182
##         [,947] [,948] [,949] [,950] [,951] [,952] [,953] [,954] [,955]
##    [1,]    138    133    125    117    109    104     99     97     98
##    [2,]    147    140    132    124    116    111    106    103    102
##    [3,]    154    145    137    129    122    115    109    105    104
##    [4,]    154    143    134    128    122    117    111    108    107
##    [5,]    159    147    136    128    122    117    113    111    110
##    [6,]    160    148    137    129    123    119    116    115    114
##    [7,]    158    145    135    128    123    121    120    119    118
##    [8,]    157    143    133    126    123    121    121    121    123
##    [9,]    155    138    128    124    122    121    121    123    131
##   [10,]    145    135    128    124    122    121    121    131    143
##   [11,]    151    137    131    124    122    121    121    142    162
##   [12,]    165    147    135    121    122    121    121    162    182
##   [13,]    182    164    152    140    125    134    156    182    180
##   [14,]    194    182    170    158    148    154    170    173    182
##   [15,]    214    196    182    176    169    171    177    179    180
##   [16,]    231    209    182    182    185    178    182    181    181
##   [17,]    243    234    213    206    204    202    196    193    187
##   [18,]    243    237    240    240    235    243    227    223    210
##   [19,]    203    219    231    241    243    242    245    244    235
##   [20,]    182    195    217    235    243    243    253    250    243
##   [21,]    182    195    215    236    255    272    286    269    252
##   [22,]    206    223    243    250    274    304    297    304    283
##   [23,]    211    243    238    250    274    286    304    302    304
##   [24,]    202    220    234    244    263    276    301    293    279
##   [25,]    182    207    215    228    243    243    243    270    263
##   [26,]    182    195    201    208    217    234    248    246    249
##   [27,]    180    182    186    188    182    203    226    243    245
##   [28,]    171    177    182    183    183    182    201    223    243
##   [29,]    160    168    179    182    180    181    182    200    221
##   [30,]    148    157    170    182    177    177    179    182    192
##   [31,]    137    146    159    166    173    173    177    182    191
##   [32,]    126    134    146    152    155    161    168    176    182
##   [33,]    121    121    132    137    138    148    159    170    179
##   [34,]    121    121    123    121    121    137    155    169    182
##   [35,]    121    121    121    121    121    121    145    165    182
##   [36,]    121    121    121    121    121    121    141    162    182
##   [37,]    121    121    121    121    121    121    141    162    182
##   [38,]    121    121    121    121    121    121    141    161    182
##   [39,]    121    121    121    121    121    126    138    156    182
##   [40,]    121    121    121    121    121    121    121    140    172
##   [41,]    121    121    121    121    121    121    121    121    149
##   [42,]    121    121    121    121    121    121    121    121    129
##   [43,]    121    121    121    121    121    121    121    121    121
##   [44,]    121    121    121    121    121    121    121    121    121
##   [45,]    145    121    121    121    121    121    121    121    121
##   [46,]    182    150    121    121    121    121    121    121    121
##   [47,]    182    175    143    121    121    121    121    121    121
##   [48,]    182    182    173    141    121    121    121    121    121
##   [49,]    182    182    182    153    121    121    121    121    121
##   [50,]    182    179    173    155    136    121    121    121    121
##   [51,]    182    174    161    148    133    121    121    121    121
##   [52,]    180    169    163    150    130    124    121    129    127
##   [53,]    182    180    182    167    149    144    145    150    156
##   [54,]    196    186    181    182    161    158    161    168    182
##   [55,]    221    205    187    178    177    178    177    180    156
##   [56,]    237    218    206    197    189    183    182    182    161
##   [57,]    244    237    223    210    198    183    183    182    166
##   [58,]    247    244    243    228    213    198    182    182    172
##   [59,]    246    244    243    243    236    216    194    182    179
##   [60,]    246    244    244    243    243    235    199    182    182
##   [61,]    217    244    243    243    243    225    193    184    183
##   [62,]    185    182    182    243    202    182    184    183    182
##   [63,]    186    183    199    187    183    185    183    183    183
##   [64,]    196    182    182    186    182    182    183    182    182
##   [65,]    209    207    192    182    188    182    182    182    182
##   [66,]    230    234    219    212    202    194    184    182    182
##   [67,]    243    245    243    229    218    207    190    182    182
##   [68,]    280    259    248    244    237    224    210    187    182
##   [69,]    304    270    250    243    243    243    231    198    182
##   [70,]    294    253    243    245    243    244    239    206    182
##   [71,]    304    304    304    274    262    247    243    214    182
##   [72,]    304    304    304    304    282    254    239    223    195
##   [73,]    298    304    304    304    294    275    243    243    224
##   [74,]    280    290    299    304    304    299    279    258    246
##   [75,]    264    274    284    294    304    304    304    273    254
##   [76,]    253    263    274    283    292    304    281    273    253
##   [77,]    240    248    258    265    272    271    263    250    242
##   [78,]    229    237    243    247    250    247    243    242    234
##   [79,]    217    227    239    243    244    244    241    235    227
##   [80,]    199    213    231    243    243    243    239    230    221
##   [81,]    182    192    229    243    243    243    240    230    217
##   [82,]    182    182    243    237    242    243    243    236    217
##   [83,]    182    192    213    243    242    243    243    232    211
##         [,956] [,957] [,958] [,959] [,960] [,961] [,962] [,963] [,964]
##    [1,]    100    102    105    108    110    111    113    117    122
##    [2,]    102    103    105    106    107    108    111    115    122
##    [3,]    104    104    105    105    105    107    110    115    122
##    [4,]    107    107    108    108    107    108    111    115    121
##    [5,]    111    111    112    111    110    111    113    116    120
##    [6,]    115    116    116    115    114    115    116    118    120
##    [7,]    119    124    125    123    120    119    119    120    121
##    [8,]    125    133    134    132    126    124    124    124    123
##    [9,]    131    144    145    142    133    132    134    131    127
##   [10,]    157    162    161    156    148    144    147    141    133
##   [11,]    170    175    175    171    165    160    161    151    140
##   [12,]    178    183    186    182    182    177    176    166    144
##   [13,]    182    186    198    200    200    194    188    177    166
##   [14,]    182    190    214    218    219    210    203    191    181
##   [15,]    182    195    236    237    237    225    217    205    194
##   [16,]    182    196    229    243    243    236    229    219    207
##   [17,]    182    204    238    242    243    242    239    232    221
##   [18,]    210    220    243    243    242    243    243    240    232
##   [19,]    231    235    242    243    243    243    243    243    241
##   [20,]    243    243    243    242    243    243    243    243    243
##   [21,]    243    244    243    243    243    243    243    241    242
##   [22,]    264    245    243    241    243    243    243    235    239
##   [23,]    271    248    239    235    236    243    216    220    232
##   [24,]    258    242    233    223    215    202    192    189    213
##   [25,]    250    236    229    215    199    182    188    183    192
##   [26,]    247    244    238    217    195    185    183    183    182
##   [27,]    244    244    243    223    182    184    182    183    182
##   [28,]    243    243    243    243    182    182    183    182    182
##   [29,]    243    243    243    243    202    182    183    183    182
##   [30,]    228    243    243    233    196    186    184    182    182
##   [31,]    213    243    243    243    223    182    183    183    182
##   [32,]    209    243    243    243    243    208    182    183    182
##   [33,]    196    232    243    243    243    220    184    182    182
##   [34,]    193    206    218    243    243    243    182    182    181
##   [35,]    183    186    187    182    213    208    191    182    181
##   [36,]    182    182    183    182    182    182    182    180    180
##   [37,]    182    182    182    181    179    179    176    177    178
##   [38,]    182    182    182    177    173    171    171    174    176
##   [39,]    182    182    182    173    165    164    167    170    174
##   [40,]    182    182    182    168    156    158    161    166    171
##   [41,]    174    182    182    161    145    144    147    156    167
##   [42,]    151    165    182    154    134    121    133    141    155
##   [43,]    136    147    142    142    121    123    121    131    142
##   [44,]    121    124    126    122    123    122    122    121    131
##   [45,]    121    121    121    121    121    121    121    121    121
##   [46,]    121    121    121    121    121    121    121    121    121
##   [47,]    121    121    121    121    121    121    121    121    121
##   [48,]    121    121    121    121    121    121    133    152    172
##   [49,]    121    121    121    121    121    121    152    182    178
##   [50,]    121    121    121    121    121    121    151    182    182
##   [51,]    121    121    121    121    121    121    150    182    182
##   [52,]    121    121    121    121    121    121    145    165    182
##   [53,]    133    121    121    121    121    121    135    162    174
##   [54,]    144    130    121    121    121    121    121    163    175
##   [55,]    148    140    132    125    121    121    142    168    177
##   [56,]    152    146    141    135    132    135    167    177    180
##   [57,]    160    155    151    147    146    147    172    179    181
##   [58,]    168    164    162    159    160    160    176    180    181
##   [59,]    177    174    173    172    175    171    178    180    181
##   [60,]    182    181    180    180    181    182    179    180    181
##   [61,]    183    182    182    182    182    182    182    182    182
##   [62,]    183    182    182    182    182    183    182    182    182
##   [63,]    182    182    182    182    182    186    185    182    182
##   [64,]    182    182    182    185    190    194    197    190    182
##   [65,]    182    182    182    190    204    214    222    218    215
##   [66,]    182    182    182    205    226    237    243    245    238
##   [67,]    182    182    197    215    243    241    250    253    253
##   [68,]    182    182    197    218    238    243    257    269    280
##   [69,]    182    182    195    215    234    243    263    281    304
##   [70,]    182    182    196    217    235    243    260    276    291
##   [71,]    182    182    201    225    243    251    260    272    286
##   [72,]    182    193    208    234    242    252    260    266    277
##   [73,]    216    211    221    236    243    248    252    255    264
##   [74,]    230    229    227    238    243    243    245    243    253
##   [75,]    243    240    238    241    243    243    243    237    241
##   [76,]    243    242    242    243    243    243    243    225    232
##   [77,]    242    240    241    243    243    223    191    206    222
##   [78,]    233    230    230    243    202    182    189    182    213
##   [79,]    220    214    206    191    183    185    183    182    190
##   [80,]    210    201    187    179    178    179    180    181    182
##   [81,]    205    194    179    170    173    175    177    180    182
##   [82,]    201    189    176    163    166    169    173    177    180
##   [83,]    188    181    166    155    158    162    168    175    180
##         [,965] [,966] [,967] [,968] [,969] [,970] [,971] [,972] [,973]
##    [1,]    129    138    147    156    164    169    173    175    176
##    [2,]    131    141    150    157    163    167    170    172    173
##    [3,]    134    146    150    156    159    162    164    166    167
##    [4,]    129    138    145    150    152    153    155    156    158
##    [5,]    125    131    137    141    143    144    145    146    148
##    [6,]    122    126    130    132    134    135    136    137    139
##    [7,]    121    122    124    125    126    127    128    129    130
##    [8,]    122    121    121    122    122    123    123    124    124
##    [9,]    124    122    121    121    121    121    121    121    121
##   [10,]    127    123    121    121    121    121    121    121    121
##   [11,]    130    125    123    122    121    121    121    121    121
##   [12,]    131    132    126    124    123    122    121    121    121
##   [13,]    153    142    137    132    127    124    123    122    121
##   [14,]    173    162    152    143    134    133    128    125    123
##   [15,]    186    177    167    160    156    145    139    131    128
##   [16,]    195    188    181    175    172    162    154    147    135
##   [17,]    210    202    196    189    184    174    168    164    156
##   [18,]    224    217    211    202    193    185    180    178    172
##   [19,]    236    231    225    217    203    195    191    188    183
##   [20,]    242    241    236    229    219    209    203    199    193
##   [21,]    243    243    242    238    232    223    216    211    204
##   [22,]    243    243    243    243    243    238    230    225    216
##   [23,]    243    243    243    243    243    243    243    243    232
##   [24,]    229    243    236    231    234    241    243    243    243
##   [25,]    211    216    218    216    219    227    243    243    243
##   [26,]    189    199    201    202    203    208    210    218    228
##   [27,]    182    182    187    188    185    182    182    195    207
##   [28,]    182    182    182    183    183    182    182    182    188
##   [29,]    182    182    182    182    182    182    182    182    191
##   [30,]    182    182    182    182    182    182    182    182    188
##   [31,]    182    182    182    182    182    182    182    182    182
##   [32,]    182    182    182    182    182    182    182    182    182
##   [33,]    182    182    182    182    182    182    182    182    182
##   [34,]    181    181    181    181    182    182    182    182    182
##   [35,]    181    181    181    181    181    182    182    182    182
##   [36,]    180    181    181    181    182    182    182    182    187
##   [37,]    179    180    181    182    182    183    185    188    194
##   [38,]    178    180    181    182    182    184    188    193    203
##   [39,]    177    180    182    182    182    185    191    198    208
##   [40,]    176    182    182    182    182    188    191    195    211
##   [41,]    173    182    182    182    182    182    182    182    207
##   [42,]    163    171    178    180    181    181    182    182    182
##   [43,]    151    162    168    175    179    181    182    182    182
##   [44,]    140    154    162    171    178    180    182    182    182
##   [45,]    129    146    156    168    177    181    182    182    182
##   [46,]    132    145    157    171    181    183    183    182    182
##   [47,]    155    165    168    178    183    188    189    188    182
##   [48,]    180    182    182    182    186    193    199    201    202
##   [49,]    182    181    182    182    188    200    210    217    221
##   [50,]    182    182    182    182    191    210    224    236    235
##   [51,]    182    182    182    182    182    226    243    239    243
##   [52,]    182    182    182    182    213    243    239    242    242
##   [53,]    178    181    182    190    212    243    243    243    243
##   [54,]    177    179    182    192    209    222    243    210    182
##   [55,]    179    180    182    182    189    204    200    197    182
##   [56,]    180    181    182    182    182    182    187    182    184
##   [57,]    181    182    182    182    182    182    182    183    182
##   [58,]    182    182    182    182    182    182    182    182    182
##   [59,]    182    182    182    182    182    182    182    182    182
##   [60,]    182    182    182    182    182    182    182    182    182
##   [61,]    182    187    182    182    182    182    182    182    182
##   [62,]    182    200    199    195    189    182    182    182    182
##   [63,]    182    212    213    209    202    192    182    182    182
##   [64,]    199    235    236    227    223    210    200    189    182
##   [65,]    222    237    243    243    243    228    214    200    185
##   [66,]    235    239    243    256    255    248    236    221    208
##   [67,]    243    243    243    272    274    265    255    238    229
##   [68,]    286    279    274    295    297    285    279    265    253
##   [69,]    301    304    304    304    304    304    304    304    304
##   [70,]    304    304    304    304    304    304    304    304    304
##   [71,]    304    304    304    304    304    304    304    304    304
##   [72,]    293    304    303    304    304    304    304    304    280
##   [73,]    277    287    299    303    304    304    304    295    270
##   [74,]    267    280    290    301    304    304    304    277    259
##   [75,]    249    266    284    302    303    304    285    259    251
##   [76,]    240    243    274    288    304    282    274    249    243
##   [77,]    240    249    264    273    275    268    257    246    243
##   [78,]    243    249    255    256    259    256    249    245    243
##   [79,]    222    243    244    241    246    248    246    235    223
##   [80,]    198    222    222    228    234    243    244    215    197
##   [81,]    197    205    201    206    212    217    216    192    186
##   [82,]    184    187    182    187    188    182    186    190    183
##   [83,]    182    182    184    182    184    182    183    182    185
##         [,974] [,975] [,976] [,977] [,978] [,979] [,980] [,981] [,982]
##    [1,]    178    179    180    182    185    188    191    193    194
##    [2,]    174    175    177    180    183    187    190    192    192
##    [3,]    168    169    172    176    180    184    188    190    190
##    [4,]    159    159    163    169    175    180    184    186    186
##    [5,]    149    149    154    162    169    176    181    183    183
##    [6,]    139    141    147    156    165    173    179    182    182
##    [7,]    131    134    143    153    164    173    179    182    182
##    [8,]    126    131    141    152    163    172    178    181    182
##    [9,]    123    128    138    150    162    171    177    181    182
##   [10,]    122    127    137    148    160    170    177    180    182
##   [11,]    121    125    134    145    157    167    176    180    183
##   [12,]    121    123    131    144    157    169    176    180    183
##   [13,]    121    121    127    140    153    166    175    180    182
##   [14,]    122    121    124    134    147    160    172    179    182
##   [15,]    124    123    122    130    143    157    170    178    181
##   [16,]    132    128    125    133    146    158    169    177    181
##   [17,]    145    138    134    143    154    164    172    178    180
##   [18,]    160    151    146    153    162    170    175    179    181
##   [19,]    172    163    159    162    168    173    177    180    182
##   [20,]    183    175    170    169    172    175    178    181    182
##   [21,]    194    187    179    176    177    178    179    182    182
##   [22,]    207    199    185    181    181    181    181    182    183
##   [23,]    223    217    204    182    188    182    182    182    187
##   [24,]    238    236    233    221    209    207    197    198    198
##   [25,]    243    243    243    243    231    229    217    224    220
##   [26,]    236    241    243    243    243    243    237    238    235
##   [27,]    218    229    239    243    243    243    243    243    243
##   [28,]    206    219    236    243    243    243    243    243    243
##   [29,]    195    208    226    243    243    243    243    243    243
##   [30,]    192    201    216    233    243    243    243    243    243
##   [31,]    182    188    200    226    239    243    243    243    243
##   [32,]    182    186    196    217    231    239    243    243    243
##   [33,]    182    182    187    211    229    242    242    243    243
##   [34,]    182    182    182    209    232    243    243    243    243
##   [35,]    182    186    209    225    238    241    242    243    243
##   [36,]    189    201    221    237    239    239    243    243    243
##   [37,]    200    215    231    243    242    243    243    243    243
##   [38,]    212    226    243    241    243    243    243    243    243
##   [39,]    221    232    243    243    242    243    243    244    245
##   [40,]    232    243    241    242    243    243    243    245    250
##   [41,]    243    243    242    243    241    243    243    247    258
##   [42,]    193    208    213    223    235    243    243    258    288
##   [43,]    182    182    182    182    222    243    239    274    304
##   [44,]    182    182    182    187    201    212    226    240    274
##   [45,]    182    182    182    182    182    197    210    234    243
##   [46,]    182    182    182    182    182    182    190    216    239
##   [47,]    188    190    182    182    182    182    182    203    234
##   [48,]    210    214    208    202    196    191    192    224    234
##   [49,]    230    243    230    221    216    214    214    228    234
##   [50,]    240    240    243    232    229    228    226    231    235
##   [51,]    242    243    243    243    244    243    239    236    238
##   [52,]    243    243    245    247    248    243    243    242    242
##   [53,]    241    243    248    255    265    267    248    243    243
##   [54,]    220    243    252    269    289    304    276    243    267
##   [55,]    190    224    243    265    292    302    304    304    294
##   [56,]    182    208    226    243    262    276    304    304    281
##   [57,]    182    201    212    222    231    238    257    255    261
##   [58,]    182    191    197    202    201    215    218    223    243
##   [59,]    182    182    184    185    183    190    188    184    182
##   [60,]    182    182    182    182    182    183    182    182    183
##   [61,]    182    182    182    182    182    182    182    182    182
##   [62,]    182    182    182    182    182    182    182    182    182
##   [63,]    182    182    182    182    182    182    182    182    182
##   [64,]    182    182    182    182    182    182    182    182    182
##   [65,]    182    182    182    182    182    182    182    182    182
##   [66,]    199    193    192    187    182    182    182    182    182
##   [67,]    222    219    223    210    198    182    182    182    182
##   [68,]    240    240    242    235    231    197    182    182    182
##   [69,]    279    250    243    243    227    216    204    200    202
##   [70,]    304    266    248    244    239    231    218    218    222
##   [71,]    277    263    243    245    243    242    237    239    243
##   [72,]    268    243    250    243    244    243    243    244    243
##   [73,]    256    251    245    244    243    243    247    250    252
##   [74,]    251    247    245    245    243    243    251    258    266
##   [75,]    249    246    245    244    243    243    255    268    284
##   [76,]    245    245    243    243    243    243    255    274    304
##   [77,]    243    243    238    242    243    243    243    252    259
##   [78,]    243    228    232    241    243    243    243    243    243
##   [79,]    218    216    224    243    243    243    243    243    243
##   [80,]    182    182    205    228    243    243    243    243    243
##   [81,]    184    182    194    218    239    243    243    243    243
##   [82,]    182    191    202    218    234    243    243    243    243
##   [83,]    182    197    211    222    239    242    243    243    243
##         [,983] [,984] [,985] [,986] [,987] [,988] [,989] [,990] [,991]
##    [1,]    194    193    193    193    193    192    191    191    191
##    [2,]    191    190    190    191    191    190    188    187    187
##    [3,]    188    187    188    190    190    188    186    185    185
##    [4,]    185    185    185    187    187    185    184    183    183
##    [5,]    183    183    183    184    185    184    183    182    182
##    [6,]    182    183    183    184    185    185    184    183    183
##    [7,]    182    184    185    187    189    189    187    186    186
##    [8,]    183    186    189    193    196    196    192    190    191
##    [9,]    184    189    195    201    205    206    200    196    197
##   [10,]    186    194    202    211    213    215    208    201    203
##   [11,]    188    199    210    220    221    223    213    204    206
##   [12,]    188    195    205    223    231    223    207    199    201
##   [13,]    184    187    193    192    200    208    197    192    193
##   [14,]    182    183    184    187    187    192    189    185    185
##   [15,]    182    182    182    182    182    184    183    182    182
##   [16,]    182    182    182    182    182    182    182    182    182
##   [17,]    182    182    182    182    182    182    182    182    182
##   [18,]    182    182    182    182    182    182    182    183    186
##   [19,]    182    182    182    182    182    182    183    189    196
##   [20,]    182    182    182    182    182    182    187    198    208
##   [21,]    183    182    182    182    182    183    194    210    221
##   [22,]    184    182    182    182    182    182    193    226    241
##   [23,]    188    182    182    182    182    182    182    224    243
##   [24,]    201    195    192    191    187    182    197    228    240
##   [25,]    218    211    212    210    204    205    218    243    259
##   [26,]    237    227    227    228    227    230    242    254    273
##   [27,]    243    243    240    243    243    243    252    273    296
##   [28,]    243    243    243    242    243    243    251    275    286
##   [29,]    243    243    243    243    243    243    248    262    270
##   [30,]    243    243    243    243    243    243    243    246    248
##   [31,]    243    243    243    243    243    243    243    243    243
##   [32,]    243    243    243    243    243    243    243    243    243
##   [33,]    243    243    243    243    243    243    246    249    254
##   [34,]    243    243    243    243    243    246    254    267    280
##   [35,]    243    243    243    243    243    247    257    266    277
##   [36,]    243    243    243    243    243    243    243    255    260
##   [37,]    243    243    243    243    243    243    243    243    243
##   [38,]    243    243    243    243    243    243    243    243    243
##   [39,]    243    243    243    243    243    243    243    243    243
##   [40,]    249    245    243    243    243    243    243    243    243
##   [41,]    259    252    243    243    243    243    243    243    243
##   [42,]    289    271    249    243    243    243    243    243    243
##   [43,]    304    304    262    243    243    243    243    243    243
##   [44,]    284    269    257    250    245    243    243    243    243
##   [45,]    243    249    247    245    245    243    243    243    243
##   [46,]    242    243    243    243    243    243    244    244    244
##   [47,]    238    241    242    243    243    243    245    245    245
##   [48,]    237    240    242    242    243    243    245    246    246
##   [49,]    237    239    242    242    243    248    251    252    251
##   [50,]    238    241    243    243    251    263    267    265    262
##   [51,]    242    243    243    243    260    293    294    285    279
##   [52,]    243    245    244    243    294    304    304    304    295
##   [53,]    250    249    247    269    296    294    291    291    291
##   [54,]    261    255    249    257    263    267    260    267    273
##   [55,]    270    257    249    244    238    237    240    249    254
##   [56,]    273    253    243    228    224    220    225    232    243
##   [57,]    250    226    212    208    206    201    206    209    216
##   [58,]    205    182    182    191    189    182    187    182    195
##   [59,]    182    188    183    182    182    184    182    184    182
##   [60,]    182    182    183    182    182    182    182    182    182
##   [61,]    182    182    182    182    182    182    182    182    182
##   [62,]    182    182    182    182    182    182    182    182    182
##   [63,]    182    182    182    182    182    193    202    202    209
##   [64,]    182    182    182    182    197    210    232    233    235
##   [65,]    182    182    182    182    199    216    227    243    243
##   [66,]    182    182    182    182    192    205    216    228    239
##   [67,]    182    182    182    182    182    192    202    217    228
##   [68,]    182    182    182    182    182    182    187    207    220
##   [69,]    198    196    186    182    182    182    200    205    217
##   [70,]    214    211    203    202    202    209    210    219    222
##   [71,]    236    231    227    233    233    235    235    236    234
##   [72,]    243    243    242    255    263    263    259    252    243
##   [73,]    251    251    262    281    293    294    283    277    270
##   [74,]    272    275    287    304    300    304    304    304    289
##   [75,]    296    298    301    302    304    304    304    304    303
##   [76,]    301    304    304    303    304    304    304    304    304
##   [77,]    285    289    288    296    296    297    301    304    298
##   [78,]    243    243    252    277    277    281    287    284    284
##   [79,]    243    243    248    261    264    266    269    273    275
##   [80,]    243    243    251    251    251    251    251    255    260
##   [81,]    243    243    243    246    246    246    246    243    244
##   [82,]    243    243    243    243    243    243    243    243    243
##   [83,]    243    243    243    243    243    243    243    243    242
##         [,992] [,993] [,994] [,995] [,996] [,997] [,998] [,999] [,1000]
##    [1,]    191    190    189    190    196    206    205    196     192
##    [2,]    187    188    188    192    206    230    240    229     218
##    [3,]    185    187    188    196    221    260    268    257     244
##    [4,]    184    186    187    195    220    259    273    265     253
##    [5,]    184    186    188    197    221    254    263    259     256
##    [6,]    186    189    193    197    211    220    230    243     246
##    [7,]    189    195    201    205    210    217    223    230     237
##    [8,]    196    204    211    215    218    221    224    228     230
##    [9,]    204    213    220    225    227    229    230    232     233
##   [10,]    212    220    227    232    235    236    237    238     238
##   [11,]    214    223    231    236    239    240    241    242     242
##   [12,]    208    220    231    237    241    242    243    243     243
##   [13,]    199    210    222    233    239    242    243    243     243
##   [14,]    190    201    214    228    237    241    243    243     243
##   [15,]    183    192    208    225    236    240    242    243     243
##   [16,]    182    185    195    214    228    237    241    243     243
##   [17,]    183    183    187    199    218    231    239    242     243
##   [18,]    188    186    185    199    217    230    238    242     243
##   [19,]    200    192    198    208    219    230    239    242     243
##   [20,]    213    213    218    223    229    236    241    243     243
##   [21,]    228    232    239    240    240    241    242    242     243
##   [22,]    243    248    258    258    250    243    243    243     243
##   [23,]    242    259    273    274    266    254    243    243     243
##   [24,]    254    272    288    289    284    273    261    249     243
##   [25,]    274    288    304    304    302    291    280    267     256
##   [26,]    289    297    298    304    304    304    292    278     269
##   [27,]    302    304    303    303    298    304    302    296     290
##   [28,]    304    304    304    304    283    289    296    298     300
##   [29,]    276    281    274    250    268    278    285    292     299
##   [30,]    243    243    249    244    257    268    279    288     299
##   [31,]    244    243    243    247    247    258    270    280     296
##   [32,]    243    246    243    252    245    243    255    260     274
##   [33,]    260    259    243    260    245    244    243    243     251
##   [34,]    304    304    304    268    245    244    243    243     243
##   [35,]    295    304    304    270    244    243    243    243     243
##   [36,]    274    275    272    253    243    243    243    243     243
##   [37,]    259    255    254    243    243    243    243    243     243
##   [38,]    243    243    243    243    243    243    243    243     243
##   [39,]    243    243    243    243    243    243    243    243     243
##   [40,]    243    243    243    243    243    243    243    253     274
##   [41,]    243    243    243    243    243    243    243    243     304
##   [42,]    243    243    243    243    243    243    246    274     297
##   [43,]    243    243    243    243    243    243    252    274     291
##   [44,]    243    243    243    243    243    243    256    276     299
##   [45,]    243    243    243    243    243    243    243    276     292
##   [46,]    243    243    243    243    243    243    243    272     295
##   [47,]    243    243    243    243    243    243    243    294     302
##   [48,]    243    243    243    243    243    243    275    304     304
##   [49,]    248    243    243    243    252    270    284    300     304
##   [50,]    259    252    243    267    272    282    292    304     302
##   [51,]    274    275    276    294    297    299    302    295     302
##   [52,]    291    293    304    301    304    304    281    285     289
##   [53,]    290    294    297    297    293    278    263    267     276
##   [54,]    275    277    275    274    266    256    243    252     264
##   [55,]    257    258    257    254    248    244    244    243     255
##   [56,]    243    243    243    243    232    236    239    242     249
##   [57,]    221    221    228    223    223    229    235    239     247
##   [58,]    200    200    205    202    210    217    226    238     245
##   [59,]    188    185    182    182    194    204    217    233     243
##   [60,]    182    183    183    182    182    188    208    227     239
##   [61,]    182    182    182    182    190    199    203    223     239
##   [62,]    189    190    191    200    202    210    217    228     241
##   [63,]    211    213    212    215    217    221    226    233     239
##   [64,]    235    236    228    229    230    230    232    236     242
##   [65,]    243    243    243    243    243    239    239    240     243
##   [66,]    243    243    243    243    243    243    247    251     265
##   [67,]    238    243    243    243    243    243    258    270     286
##   [68,]    232    242    243    243    243    260    267    283     304
##   [69,]    234    243    243    256    269    278    288    295     313
##   [70,]    233    241    243    272    289    304    304    304     345
##   [71,]    238    254    273    294    302    302    304    316     351
##   [72,]    250    271    286    292    304    303    304    320     339
##   [73,]    271    280    289    296    300    304    304    309     314
##   [74,]    289    293    295    299    304    302    304    304     304
##   [75,]    301    304    304    304    304    304    304    304     304
##   [76,]    304    304    304    304    304    304    304    304     304
##   [77,]    302    304    304    304    304    304    304    304     304
##   [78,]    293    301    304    304    304    304    304    304     304
##   [79,]    287    298    302    304    304    304    304    304     304
##   [80,]    281    301    303    304    304    304    304    304     298
##   [81,]    263    286    304    304    304    304    295    289     282
##   [82,]    248    268    281    296    304    287    279    273     266
##   [83,]    243    255    259    269    269    263    262    259     253
##         [,1001] [,1002] [,1003] [,1004] [,1005] [,1006] [,1007] [,1008]
##    [1,]     185     184     185     189     193     196     199     200
##    [2,]     208     202     199     200     200     200     201     202
##    [3,]     232     220     214     212     210     209     206     205
##    [4,]     242     232     228     224     222     219     214     211
##    [5,]     248     240     237     234     231     227     220     215
##    [6,]     243     241     241     238     235     230     222     214
##    [7,]     236     236     236     234     232     228     221     213
##    [8,]     232     232     231     229     227     224     218     211
##    [9,]     233     232     230     226     222     219     214     208
##   [10,]     238     236     231     225     219     214     209     205
##   [11,]     241     238     230     221     214     209     207     208
##   [12,]     243     239     226     214     208     209     212     218
##   [13,]     243     240     229     223     219     220     221     232
##   [14,]     243     243     238     233     230     230     232     237
##   [15,]     243     243     243     241     238     239     240     241
##   [16,]     243     243     243     243     243     243     243     241
##   [17,]     243     243     243     244     246     245     244     240
##   [18,]     243     243     245     251     253     249     246     243
##   [19,]     243     244     251     261     266     255     252     246
##   [20,]     243     246     261     276     281     273     262     257
##   [21,]     243     248     274     286     293     290     281     275
##   [22,]     243     243     261     282     297     303     299     296
##   [23,]     243     243     249     270     287     300     304     304
##   [24,]     243     243     243     260     286     304     303     304
##   [25,]     243     243     243     260     287     297     302     303
##   [26,]     268     271     280     285     298     300     301     302
##   [27,]     291     300     304     302     303     304     304     304
##   [28,]     301     303     303     304     304     304     304     304
##   [29,]     302     304     304     304     304     304     304     304
##   [30,]     304     304     304     304     304     304     304     304
##   [31,]     304     304     304     304     304     304     304     299
##   [32,]     290     304     304     304     304     304     304     293
##   [33,]     271     290     304     293     288     293     304     263
##   [34,]     253     266     270     267     256     243     243     213
##   [35,]     243     249     252     243     243     182     232     216
##   [36,]     243     243     229     182     190     204     209     204
##   [37,]     243     243     217     202     182     182     195     190
##   [38,]     243     243     224     213     210     200     192     187
##   [39,]     243     243     234     228     229     225     216     205
##   [40,]     256     249     243     242     252     249     237     226
##   [41,]     295     279     272     280     280     278     293     253
##   [42,]     304     304     300     303     304     310     316     287
##   [43,]     302     304     304     304     304     311     307     304
##   [44,]     303     303     304     304     294     288     301     304
##   [45,]     304     304     304     304     274     243     268     275
##   [46,]     304     304     304     304     275     243     248     253
##   [47,]     303     304     304     304     284     253     243     245
##   [48,]     304     303     304     304     304     268     239     216
##   [49,]     304     304     304     304     287     269     236     210
##   [50,]     304     304     304     304     294     270     250     225
##   [51,]     300     302     304     304     295     276     254     243
##   [52,]     289     291     291     285     278     265     249     228
##   [53,]     275     277     274     268     258     247     245     233
##   [54,]     263     263     263     259     243     244     244     243
##   [55,]     260     263     267     271     270     244     243     251
##   [56,]     264     273     282     293     304     267     270     279
##   [57,]     264     276     288     304     300     300     295     304
##   [58,]     258     271     286     299     304     304     304     303
##   [59,]     252     261     280     291     299     304     304     304
##   [60,]     243     248     274     287     297     303     304     304
##   [61,]     243     256     270     284     297     303     304     304
##   [62,]     243     253     269     285     301     304     304     306
##   [63,]     242     243     268     286     296     304     304     308
##   [64,]     249     262     274     288     301     304     304     307
##   [65,]     262     275     288     304     303     303     304     304
##   [66,]     274     285     299     304     304     304     304     304
##   [67,]     288     294     304     304     304     304     304     304
##   [68,]     297     299     304     306     305     304     304     304
##   [69,]     320     318     314     311     306     304     304     304
##   [70,]     365     350     339     325     312     304     304     304
##   [71,]     362     365     359     339     319     307     304     302
##   [72,]     365     365     347     341     319     304     301     295
##   [73,]     328     334     331     326     315     305     297     283
##   [74,]     304     315     314     320     319     311     304     274
##   [75,]     304     304     307     334     328     321     309     294
##   [76,]     304     304     304     365     346     340     318     304
##   [77,]     304     304     304     348     365     365     325     304
##   [78,]     304     303     304     330     352     340     328     315
##   [79,]     304     301     302     304     320     322     321     313
##   [80,]     297     296     299     310     310     310     311     309
##   [81,]     281     280     286     300     308     309     306     306
##   [82,]     260     253     267     285     304     305     305     305
##   [83,]     243     246     243     267     288     304     304     304
##         [,1009] [,1010] [,1011] [,1012] [,1013] [,1014] [,1015] [,1016]
##    [1,]     200     199     207     198     179     159     142     127
##    [2,]     204     211     229     221     197     168     146     129
##    [3,]     207     219     238     224     193     161     136     121
##    [4,]     210     219     239     227     197     166     142     125
##    [5,]     211     207     218     203     179     156     137     123
##    [6,]     206     196     174     154     142     133     126     119
##    [7,]     204     187     163     145     134     128     123     118
##    [8,]     199     182     157     140     131     126     123     120
##    [9,]     198     183     160     144     136     131     127     124
##   [10,]     201     190     168     153     146     140     134     130
##   [11,]     212     206     189     173     161     152     144     139
##   [12,]     226     225     211     197     179     166     156     148
##   [13,]     235     235     219     201     183     172     165     160
##   [14,]     239     229     214     198     188     179     174     171
##   [15,]     238     221     202     193     187     183     181     180
##   [16,]     231     214     198     189     186     185     185     184
##   [17,]     227     205     197     192     193     193     196     189
##   [18,]     232     219     207     203     206     209     206     195
##   [19,]     240     231     226     220     223     233     226     210
##   [20,]     251     244     242     239     240     242     239     226
##   [21,]     264     254     258     259     255     252     249     241
##   [22,]     284     274     275     279     268     261     256     249
##   [23,]     302     296     296     304     278     269     263     255
##   [24,]     304     302     304     304     283     276     269     260
##   [25,]     304     304     304     291     287     281     275     265
##   [26,]     304     304     304     299     293     285     274     264
##   [27,]     304     304     304     304     301     289     274     263
##   [28,]     304     304     304     304     304     291     271     259
##   [29,]     304     304     304     304     304     281     258     253
##   [30,]     303     304     304     304     276     263     239     243
##   [31,]     295     297     291     273     253     236     203     186
##   [32,]     280     277     268     258     243     218     184     183
##   [33,]     262     258     260     253     243     228     195     183
##   [34,]     243     243     249     247     246     244     222     190
##   [35,]     182     182     243     243     243     244     237     207
##   [36,]     187     183     183     182     203     230     238     218
##   [37,]     184     184     183     181     181     192     225     224
##   [38,]     183     183     182     180     178     179     191     195
##   [39,]     189     182     182     178     174     170     164     159
##   [40,]     204     189     182     175     168     158     144     128
##   [41,]     224     205     182     177     167     153     138     121
##   [42,]     253     233     201     182     174     161     149     142
##   [43,]     273     243     208     190     182     172     165     164
##   [44,]     270     243     202     182     186     181     178     182
##   [45,]     260     238     182     184     183     188     201     209
##   [46,]     243     215     182     182     182     203     243     243
##   [47,]     230     206     182     182     182     213     241     242
##   [48,]     202     182     191     183     200     223     243     243
##   [49,]     182     184     183     184     208     241     241     243
##   [50,]     200     182     182     182     182     243     243     243
##   [51,]     210     182     182     182     182     192     223     236
##   [52,]     216     203     182     182     182     182     182     202
##   [53,]     224     220     205     189     182     182     182     182
##   [54,]     241     243     224     205     182     182     182     204
##   [55,]     243     248     243     223     191     182     182     206
##   [56,]     293     268     244     238     211     197     206     217
##   [57,]     299     304     274     243     228     226     228     232
##   [58,]     304     303     304     275     247     238     240     250
##   [59,]     304     305     304     284     260     243     262     269
##   [60,]     304     308     309     302     282     281     287     289
##   [61,]     308     313     316     315     304     298     322     302
##   [62,]     313     319     326     334     338     335     355     335
##   [63,]     315     324     333     350     365     363     365     360
##   [64,]     308     320     332     356     364     365     364     365
##   [65,]     304     304     318     340     365     347     352     351
##   [66,]     304     304     304     324     325     328     321     323
##   [67,]     304     304     304     305     305     304     304     304
##   [68,]     304     303     304     304     304     305     304     317
##   [69,]     303     303     303     304     304     311     327     339
##   [70,]     302     301     302     304     314     328     350     365
##   [71,]     298     293     297     304     317     330     346     359
##   [72,]     286     277     283     296     304     308     304     325
##   [73,]     266     252     267     284     294     302     305     304
##   [74,]     243     248     251     273     287     300     304     319
##   [75,]     256     243     245     263     285     304     303     319
##   [76,]     277     243     243     243     270     296     304     320
##   [77,]     284     243     243     243     243     278     304     316
##   [78,]     304     258     243     243     249     267     287     304
##   [79,]     304     274     243     243     252     266     283     304
##   [80,]     304     275     243     243     243     250     280     301
##   [81,]     304     280     252     243     243     243     274     304
##   [82,]     304     277     243     243     243     258     277     304
##   [83,]     304     287     243     243     243     243     274     288
##         [,1017] [,1018] [,1019] [,1020] [,1021] [,1022] [,1023] [,1024]
##    [1,]     116     109     108     109     112     116     120     124
##    [2,]     117     108     106     107     110     114     118     123
##    [3,]     112     107     105     106     108     113     118     121
##    [4,]     114     107     105     105     107     111     115     117
##    [5,]     113     108     106     105     106     108     110     111
##    [6,]     113     109     107     106     105     105     105     104
##    [7,]     114     111     109     107     105     103     100      96
##    [8,]     117     113     111     109     107     104      97      91
##    [9,]     120     117     115     113     112     107      97      88
##   [10,]     125     122     120     119     117     111     101      89
##   [11,]     132     126     123     121     120     115     105      94
##   [12,]     139     132     127     123     121     119     111      99
##   [13,]     152     142     132     126     122     119     109      99
##   [14,]     166     155     142     131     124     120     110      99
##   [15,]     176     166     150     135     127     125     114     103
##   [16,]     182     170     149     135     132     139     129     117
##   [17,]     184     174     160     141     149     165     160     141
##   [18,]     188     181     173     167     174     178     179     170
##   [19,]     197     191     188     187     186     189     188     184
##   [20,]     216     206     205     205     199     198     193     188
##   [21,]     233     225     224     220     212     205     194     190
##   [22,]     243     243     243     234     225     214     208     196
##   [23,]     249     246     244     243     239     232     234     219
##   [24,]     253     249     245     243     242     242     243     243
##   [25,]     256     251     246     243     240     240     243     243
##   [26,]     257     252     247     243     231     220     243     243
##   [27,]     256     251     245     238     216     188     199     228
##   [28,]     254     249     246     243     214     182     183     182
##   [29,]     251     248     245     244     236     185     179     179
##   [30,]     246     246     245     243     182     186     176     174
##   [31,]     213     244     232     212     199     181     173     170
##   [32,]     185     182     206     195     181     173     168     164
##   [33,]     182     183     182     182     180     169     162     156
##   [34,]     182     182     182     182     176     165     157     149
##   [35,]     196     182     182     182     174     161     151     141
##   [36,]     218     216     201     186     176     163     151     138
##   [37,]     243     243     227     194     184     173     157     143
##   [38,]     199     213     213     187     183     174     161     148
##   [39,]     142     121     152     152     158     157     149     144
##   [40,]     123     125     122     121     130     133     133     132
##   [41,]     121     122     121     122     122     121     121     123
##   [42,]     130     121     121     121     124     129     125     121
##   [43,]     159     140     121     121     131     141     135     126
##   [44,]     182     161     148     121     149     154     144     128
##   [45,]     200     192     186     164     167     143     152     126
##   [46,]     226     216     205     196     182     121     159     121
##   [47,]     243     237     225     219     179     156     175     172
##   [48,]     243     243     243     243     215     207     198     182
##   [49,]     243     243     243     243     243     227     213     201
##   [50,]     243     243     243     243     243     236     226     212
##   [51,]     243     243     243     243     246     245     238     226
##   [52,]     224     238     243     243     251     255     250     243
##   [53,]     211     234     243     245     256     264     258     250
##   [54,]     217     238     250     262     276     290     276     263
##   [55,]     225     243     261     285     304     302     304     284
##   [56,]     231     240     267     299     309     315     313     308
##   [57,]     243     262     291     311     321     329     329     321
##   [58,]     262     275     297     326     339     352     353     339
##   [59,]     281     292     314     340     365     362     365     365
##   [60,]     298     312     332     352     361     364     364     365
##   [61,]     304     333     356     365     363     365     364     365
##   [62,]     355     355     361     364     365     365     365     365
##   [63,]     365     365     365     365     364     365     365     365
##   [64,]     364     365     365     365     365     365     365     365
##   [65,]     358     365     365     365     365     365     365     365
##   [66,]     329     345     365     365     365     365     365     365
##   [67,]     304     333     359     364     365     365     365     365
##   [68,]     326     345     365     365     364     365     365     371
##   [69,]     347     361     364     364     365     365     370     379
##   [70,]     365     364     365     365     365     365     374     386
##   [71,]     365     364     365     365     365     365     364     377
##   [72,]     342     359     365     365     365     365     361     363
##   [73,]     329     356     364     365     365     357     351     354
##   [74,]     329     356     365     365     365     340     321     339
##   [75,]     336     357     365     365     365     333     304     318
##   [76,]     339     362     365     365     351     328     304     309
##   [77,]     352     365     365     337     324     304     313     305
##   [78,]     334     346     332     314     306     307     305     304
##   [79,]     318     319     312     304     304     305     304     300
##   [80,]     304     308     305     305     304     304     304     293
##   [81,]     304     304     304     305     304     304     304     286
##   [82,]     304     304     304     304     304     304     297     275
##   [83,]     304     304     304     304     304     304     277     256
##         [,1025] [,1026] [,1027] [,1028] [,1029] [,1030] [,1031] [,1032]
##    [1,]     127     129     132     135     137     138     137     133
##    [2,]     126     128     132     137     139     140     139     136
##    [3,]     124     126     131     135     139     141     140     137
##    [4,]     119     120     125     130     135     137     137     136
##    [5,]     112     112     116     122     128     132     133     132
##    [6,]     102     102     106     113     119     125     127     127
##    [7,]      93      92      96     102     109     117     122     124
##    [8,]      85      83      85      91     100     109     116     120
##    [9,]      80      75      75      81      91     102     109     114
##   [10,]      79      72      69      74      85      92      98     105
##   [11,]      82      72      66      67      75      81      87      94
##   [12,]      86      73      66      63      65      70      71      81
##   [13,]      88      77      67      63      62      62      62      70
##   [14,]      89      77      68      63      61      60      60      62
##   [15,]      91      76      71      65      62      61      60      60
##   [16,]     105      94      82      71      66      63      61      60
##   [17,]     126     115     106      89      74      70      64      62
##   [18,]     159     140     131     117      98      83      71      68
##   [19,]     172     173     156     140     124     107      91      76
##   [20,]     183     178     167     151     136     121     108      96
##   [21,]     184     180     170     157     142     131     121     111
##   [22,]     182     182     176     170     149     121     131     121
##   [23,]     203     191     189     185     171     152     162     152
##   [24,]     222     212     209     200     190     185     183     183
##   [25,]     238     228     226     217     200     189     185     183
##   [26,]     243     243     243     233     206     190     185     183
##   [27,]     243     243     243     234     204     185     183     182
##   [28,]     213     243     243     211     182     185     183     183
##   [29,]     180     181     194     194     188     184     183     182
##   [30,]     174     176     179     182     183     183     183     182
##   [31,]     170     172     174     178     182     182     182     182
##   [32,]     164     165     167     171     178     182     182     182
##   [33,]     158     158     159     165     173     182     182     182
##   [34,]     146     144     144     152     162     169     172     165
##   [35,]     130     121     121     136     148     154     153     150
##   [36,]     126     122     122     124     135     138     137     137
##   [37,]     133     127     121     121     121     121     121     125
##   [38,]     137     128     121     121     121     121     121     121
##   [39,]     136     128     121     121     121     121     121     121
##   [40,]     129     125     123     121     121     121     121     121
##   [41,]     123     123     122     122     121     121     121     121
##   [42,]     121     122     122     121     121     121     121     121
##   [43,]     123     122     121     121     121     121     121     121
##   [44,]     124     122     121     121     121     121     121     121
##   [45,]     122     122     121     121     121     121     121     121
##   [46,]     121     121     121     121     121     121     121     121
##   [47,]     148     130     121     121     121     121     121     121
##   [48,]     182     162     128     121     121     121     121     126
##   [49,]     189     173     130     121     121     121     121     126
##   [50,]     198     172     121     121     121     121     121     151
##   [51,]     211     189     155     121     121     121     121     149
##   [52,]     229     204     182     182     121     121     121     145
##   [53,]     243     217     203     191     182     121     158     154
##   [54,]     249     237     224     217     209     195     187     177
##   [55,]     266     248     243     243     243     226     211     195
##   [56,]     294     292     290     263     251     245     235     207
##   [57,]     313     304     287     276     261     249     244     227
##   [58,]     325     307     294     279     263     246     244     225
##   [59,]     344     321     304     284     266     243     243     231
##   [60,]     356     329     310     299     279     267     252     239
##   [61,]     361     340     321     304     294     288     281     265
##   [62,]     365     349     330     304     304     304     304     282
##   [63,]     365     365     355     349     325     323     317     303
##   [64,]     366     366     365     366     365     346     338     322
##   [65,]     367     369     368     368     366     361     359     343
##   [66,]     369     372     372     372     370     366     365     365
##   [67,]     371     377     378     378     377     366     365     354
##   [68,]     379     387     391     395     399     381     365     359
##   [69,]     396     408     412     420     426     406     378     366
##   [70,]     414     426     423     420     426     426     384     367
##   [71,]     409     426     418     410     407     398     378     364
##   [72,]     385     385     392     380     365     373     359     349
##   [73,]     365     365     372     365     363     365     345     333
##   [74,]     365     365     365     349     336     333     325     310
##   [75,]     365     365     365     334     304     313     308     309
##   [76,]     352     365     352     330     304     304     304     304
##   [77,]     325     329     332     316     304     302     302     303
##   [78,]     310     311     308     300     297     299     301     303
##   [79,]     300     304     292     287     291     295     299     302
##   [80,]     289     282     277     275     280     289     297     301
##   [81,]     275     266     262     263     271     284     296     301
##   [82,]     259     249     248     253     265     282     297     302
##   [83,]     243     246     243     243     263     285     301     303
##         [,1033] [,1034] [,1035] [,1036] [,1037] [,1038] [,1039] [,1040]
##    [1,]     126     117     106      95      82      71      61      53
##    [2,]     130     121     111      99      86      75      65      57
##    [3,]     131     122     110      97      85      75      66      60
##    [4,]     131     121     108      95      84      74      66      61
##    [5,]     128     120     109      97      85      75      67      62
##    [6,]     126     120     110      98      86      76      68      63
##    [7,]     124     119     110      99      88      78      70      63
##    [8,]     121     119     113     104      93      81      71      64
##    [9,]     117     118     115     106      95      83      73      65
##   [10,]     110     115     116     109      98      85      74      65
##   [11,]     101     109     115     108      97      84      73      65
##   [12,]      91     105     109     108      92      76      67      62
##   [13,]      73      80      90      77      67      68      63      60
##   [14,]      62      66      67      69      64      62      60      59
##   [15,]      60      60      63      62      61      60      60      60
##   [16,]      60      60      61      61      61      60      62      62
##   [17,]      61      62      64      64      63      64      73      72
##   [18,]      65      72      76      74      70      77      87      92
##   [19,]      76      86      92      93      99     103     114     119
##   [20,]      92     106     111     115     124     136     144     146
##   [21,]     113     123     131     139     150     162     173     174
##   [22,]     121     150     150     157     166     182     179     182
##   [23,]     172     174     169     165     169     182     182     182
##   [24,]     182     175     176     162     158     165     182     182
##   [25,]     182     182     160     143     131     134     153     174
##   [26,]     183     182     146     121     125     122     121     149
##   [27,]     182     168     136     123     122     122     121     121
##   [28,]     182     182     158     121     121     121     121     121
##   [29,]     182     182     182     121     121     121     121     121
##   [30,]     182     182     174     158     137     121     121     121
##   [31,]     182     182     182     182     182     152     121     121
##   [32,]     182     182     182     182     182     182     171     146
##   [33,]     179     182     182     182     182     182     182     163
##   [34,]     167     172     182     182     182     182     182     169
##   [35,]     152     159     172     182     177     182     182     182
##   [36,]     136     143     155     155     158     168     172     160
##   [37,]     121     126     138     138     136     150     152     148
##   [38,]     122     121     123     124     121     135     136     136
##   [39,]     121     121     121     121     121     121     125     126
##   [40,]     121     121     121     121     121     121     121     123
##   [41,]     121     121     121     121     121     121     121     121
##   [42,]     121     121     121     121     121     121     121     121
##   [43,]     121     121     121     121     121     121     121     121
##   [44,]     121     121     121     121     121     121     121     121
##   [45,]     121     121     121     121     121     121     121     121
##   [46,]     121     121     121     121     121     121     121     121
##   [47,]     123     133     135     131     131     126     121     121
##   [48,]     143     162     163     158     162     149     137     121
##   [49,]     167     180     182     179     182     174     170     141
##   [50,]     181     182     181     183     185     186     186     168
##   [51,]     174     182     182     184     187     191     191     182
##   [52,]     167     182     182     186     192     200     206     198
##   [53,]     167     177     182     188     197     209     224     217
##   [54,]     174     178     181     186     202     220     239     237
##   [55,]     181     180     181     182     194     224     243     242
##   [56,]     182     182     181     182     182     235     241     243
##   [57,]     196     182     182     182     182     243     242     243
##   [58,]     208     196     182     182     182     219     243     243
##   [59,]     219     211     198     182     215     243     240     244
##   [60,]     237     235     220     224     228     243     243     245
##   [61,]     257     249     243     238     243     245     246     246
##   [62,]     270     261     252     243     255     251     250     249
##   [63,]     288     278     271     269     270     264     261     259
##   [64,]     304     294     291     285     284     279     277     276
##   [65,]     322     310     304     300     296     294     297     297
##   [66,]     338     320     304     304     304     304     305     307
##   [67,]     344     332     321     310     304     304     310     311
##   [68,]     350     344     335     325     315     311     315     315
##   [69,]     361     360     350     340     329     327     323     321
##   [70,]     366     365     365     355     345     340     334     333
##   [71,]     365     365     365     365     355     350     346     347
##   [72,]     353     365     365     365     365     362     362     369
##   [73,]     331     348     365     365     365     365     384     396
##   [74,]     306     315     339     358     365     383     400     426
##   [75,]     304     304     316     338     360     375     398     412
##   [76,]     304     304     304     325     351     365     390     402
##   [77,]     304     304     304     324     350     365     384     392
##   [78,]     304     304     321     336     361     371     377     381
##   [79,]     304     304     319     335     357     364     367     368
##   [80,]     304     304     309     321     338     353     355     352
##   [81,]     303     304     304     304     319     323     324     321
##   [82,]     303     304     304     304     304     304     304     304
##   [83,]     304     304     304     304     304     304     304     304
##         [,1041] [,1042] [,1043] [,1044] [,1045] [,1046] [,1047] [,1048]
##    [1,]      48      45      43      42      42      43      45      48
##    [2,]      53      51      50      49      49      51      52      54
##    [3,]      57      56      55      55      55      57      58      59
##    [4,]      58      57      57      56      56      58      59      60
##    [5,]      59      57      57      56      57      58      59      60
##    [6,]      59      57      57      56      57      58      59      60
##    [7,]      59      57      57      57      58      58      59      60
##    [8,]      60      58      58      58      58      59      59      60
##    [9,]      60      58      58      59      59      59      59      60
##   [10,]      60      58      58      59      59      59      60      60
##   [11,]      60      58      58      59      59      59      60      60
##   [12,]      60      59      59      59      59      59      60      60
##   [13,]      59      59      59      59      59      59      60      60
##   [14,]      59      59      59      60      60      60      60      60
##   [15,]      60      60      60      60      60      60      60      60
##   [16,]      62      60      60      69      64      60      60      60
##   [17,]      74      75      84      97      84      69      60      60
##   [18,]      94      89     103     121      99      78      60      60
##   [19,]     120     115     124     124     121      97      71      60
##   [20,]     147     155     144     143     132     121      96      60
##   [21,]     174     182     174     172     154     129     121      87
##   [22,]     182     182     182     182     182     121     113      93
##   [23,]     182     182     182     182     168     145     126     110
##   [24,]     182     182     182     175     156     132     121     106
##   [25,]     182     182     182     176     146     127     122     109
##   [26,]     182     182     182     157     145     131     124     121
##   [27,]     152     162     154     146     140     129     121     104
##   [28,]     121     121     121     121     127     121     107      81
##   [29,]     121     121     121     121     121     117     102      80
##   [30,]     121     121     121     121     121     114     105      87
##   [31,]     121     121     121     121     121     116     111      94
##   [32,]     128     122     121     121     121     121     121     105
##   [33,]     137     123     121     121     121     121     121     106
##   [34,]     136     122     122     121     121     121     121     110
##   [35,]     141     121     121     121     121     121     121     120
##   [36,]     143     129     121     121     121     121     121     121
##   [37,]     141     129     121     121     121     121     121     121
##   [38,]     133     128     121     121     121     121     121     121
##   [39,]     127     125     121     121     121     121     121     121
##   [40,]     124     123     121     121     121     121     121     121
##   [41,]     122     122     121     121     121     121     121     121
##   [42,]     121     121     121     121     121     121     121     121
##   [43,]     121     121     121     121     121     121     121     121
##   [44,]     121     121     121     121     121     121     121     121
##   [45,]     121     121     121     121     121     121     121     121
##   [46,]     121     121     121     121     121     121     121     121
##   [47,]     121     121     121     121     123     122     121     121
##   [48,]     121     121     121     121     126     125     123     121
##   [49,]     127     121     121     131     130     127     124     122
##   [50,]     148     142     142     138     136     131     125     122
##   [51,]     170     161     156     150     144     137     127     123
##   [52,]     188     177     169     160     153     144     127     122
##   [53,]     206     193     182     171     164     155     121     123
##   [54,]     225     210     200     188     180     183     167     137
##   [55,]     243     225     217     206     199     188     183     182
##   [56,]     243     239     237     225     209     192     183     182
##   [57,]     243     243     243     243     205     182     183     182
##   [58,]     243     243     243     230     199     182     182     182
##   [59,]     241     240     240     243     199     182     182     182
##   [60,]     239     236     235     243     198     182     182     182
##   [61,]     241     235     232     195     182     183     183     182
##   [62,]     247     243     224     219     193     182     182     182
##   [63,]     257     249     238     232     224     197     182     182
##   [64,]     275     269     259     243     245     223     201     182
##   [65,]     297     295     292     278     257     243     224     210
##   [66,]     306     306     305     304     272     243     243     238
##   [67,]     309     308     306     305     288     243     243     243
##   [68,]     313     310     307     305     277     262     243     243
##   [69,]     317     313     309     297     281     272     258     243
##   [70,]     327     320     313     301     291     287     276     270
##   [71,]     338     329     319     308     301     299     298     304
##   [72,]     358     344     331     311     304     304     310     310
##   [73,]     388     365     350     328     304     323     324     324
##   [74,]     426     410     380     350     342     344     339     338
##   [75,]     426     426     426     377     365     365     361     365
##   [76,]     411     419     416     414     411     391     381     379
##   [77,]     398     405     413     425     426     426     412     408
##   [78,]     382     387     397     415     426     428     431     427
##   [79,]     365     365     385     404     415     426     427     428
##   [80,]     354     356     371     393     403     414     426     426
##   [81,]     326     331     357     375     382     387     396     381
##   [82,]     304     304     341     365     366     365     366     365
##   [83,]     304     309     318     342     356     360     363     365
##         [,1049] [,1050] [,1051] [,1052] [,1053] [,1054] [,1055] [,1056]
##    [1,]      51      56      60      62      63      62      60      58
##    [2,]      57      61      65      67      66      64      61      58
##    [3,]      62      66      69      69      68      65      62      58
##    [4,]      63      67      69      69      68      65      62      60
##    [5,]      62      66      67      67      66      64      62      61
##    [6,]      61      64      65      64      64      63      61      60
##    [7,]      60      61      62      62      62      61      61      60
##    [8,]      60      60      61      61      61      61      61      60
##    [9,]      60      60      60      60      60      60      60      60
##   [10,]      60      60      60      60      60      60      60      60
##   [11,]      60      60      60      60      60      60      60      60
##   [12,]      60      60      60      60      60      60      60      60
##   [13,]      60      60      60      60      60      60      60      60
##   [14,]      60      60      60      60      60      60      60      60
##   [15,]      60      60      60      60      60      60      60      60
##   [16,]      60      60      60      60      60      60      60      60
##   [17,]      60      60      60      60      60      60      60      60
##   [18,]      60      60      60      60      60      60      60      60
##   [19,]      60      60      60      60      60      60      60      60
##   [20,]      60      60      60      60      60      60      60      60
##   [21,]      60      60      60      60      60      60      60      60
##   [22,]      60      60      60      60      60      60      60      60
##   [23,]      66      60      60      60      60      60      60      60
##   [24,]      84      60      60      60      60      60      60      77
##   [25,]      77      60      60      60      60      60      63      85
##   [26,]      75      60      61      61      60      60      60      94
##   [27,]      60      67      62      61      60      60      60      93
##   [28,]      62      61      62      62      61      60      65      96
##   [29,]      60      62      61      60      61      60      70      99
##   [30,]      69      60      60      60      60      60      82     115
##   [31,]      73      60      60      60      60      73     109     121
##   [32,]      80      67      60      60      67      92     121     150
##   [33,]      90      81      72      60      82     103     121     154
##   [34,]     102      96      90      97     100     120     143     164
##   [35,]     116     113     111     110     113     130     153     182
##   [36,]     121     119     119     118     118     129     149     162
##   [37,]     121     121     121     121     121     123     129     144
##   [38,]     121     121     121     121     121     121     121     121
##   [39,]     121     121     121     121     121     121     121     121
##   [40,]     121     121     121     121     121     121     121     121
##   [41,]     121     121     121     121     121     121     121     121
##   [42,]     121     121     121     121     121     121     121     121
##   [43,]     121     121     121     121     121     121     121     121
##   [44,]     121     121     121     121     121     121     121     121
##   [45,]     121     121     121     121     121     121     121     121
##   [46,]     121     121     121     121     121     121     121     121
##   [47,]     121     121     121     121     121     121     121     121
##   [48,]     121     121     121     121     121     121     121     121
##   [49,]     121     121     121     121     121     121     121     121
##   [50,]     121     121     121     121     121     121     121     121
##   [51,]     121     121     121     121     121     121     121     121
##   [52,]     122     121     121     121     121     121     121     121
##   [53,]     121     121     121     121     121     121     121     121
##   [54,]     122     121     121     121     121     121     121     125
##   [55,]     182     131     121     121     121     121     133     134
##   [56,]     163     148     129     121     121     135     145     146
##   [57,]     165     151     142     128     139     146     160     171
##   [58,]     168     157     149     145     148     160     170     182
##   [59,]     174     167     163     163     168     172     182     184
##   [60,]     182     180     178     182     178     178     182     192
##   [61,]     182     182     182     184     185     181     191     203
##   [62,]     182     182     182     189     196     203     208     220
##   [63,]     182     182     192     202     213     220     227     233
##   [64,]     182     182     221     232     231     235     238     240
##   [65,]     202     219     241     243     243     243     243     242
##   [66,]     235     243     241     245     243     243     243     243
##   [67,]     242     241     245     247     244     243     240     228
##   [68,]     243     243     248     255     243     243     231     211
##   [69,]     243     243     262     276     265     248     243     213
##   [70,]     260     269     289     302     292     261     243     217
##   [71,]     295     294     301     303     304     270     243     219
##   [72,]     306     303     304     303     294     253     242     228
##   [73,]     316     308     304     304     304     243     243     242
##   [74,]     326     308     305     296     275     243     243     243
##   [75,]     338     305     304     294     278     264     243     284
##   [76,]     372     337     315     309     297     282     291     300
##   [77,]     401     374     348     332     317     304     301     295
##   [78,]     426     412     377     357     342     327     311     291
##   [79,]     426     426     411     380     365     350     333     311
##   [80,]     426     426     426     384     372     365     347     316
##   [81,]     381     406     381     375     371     368     366     345
##   [82,]     365     372     371     368     367     366     366     365
##   [83,]     365     367     368     367     366     366     365     365
##         [,1057] [,1058] [,1059] [,1060] [,1061] [,1062] [,1063] [,1064]
##    [1,]      55      52      49      46      43      41      39      37
##    [2,]      55      52      50      47      44      42      40      39
##    [3,]      55      53      51      48      45      43      42      41
##    [4,]      57      54      53      50      47      46      46      45
##    [5,]      59      56      55      52      50      50      50      49
##    [6,]      59      58      57      55      54      55      54      52
##    [7,]      60      60      59      59      59      59      58      56
##    [8,]      60      60      60      60      60      60      60      59
##    [9,]      60      60      60      60      60      60      60      60
##   [10,]      60      60      60      60      60      61      61      60
##   [11,]      60      60      60      60      61      62      63      61
##   [12,]      60      60      60      61      62      66      69      64
##   [13,]      60      60      60      62      65      73      79      72
##   [14,]      60      60      60      63      68      80      86      76
##   [15,]      60      60      60      65      75      93      98      80
##   [16,]      60      60      60      68      83     111     107      82
##   [17,]      60      60      60      66      88     121     118      83
##   [18,]      60      60      60      60      60     105      94      81
##   [19,]      60      60      60      60      60      65      81      70
##   [20,]      60      60      60      60      60      60      60      62
##   [21,]      60      60      60      60      60      60      60      60
##   [22,]      60      60      60      60      60      60      60      60
##   [23,]      69      67      60      60      60      60      60      60
##   [24,]      88      94      85      70      60      60      60      60
##   [25,]     106     121     104      89      72      60      60      60
##   [26,]     114     119     121     113      92      72      60      60
##   [27,]     109     115     121     111     101      78      60      60
##   [28,]     111     118     119     118     115      99      84      68
##   [29,]     113     121     121     121     122     121     106      91
##   [30,]     132     140     140     149     135     122     121     114
##   [31,]     162     182     182     182     151     128     122     121
##   [32,]     182     179     182     182     159     129     122     121
##   [33,]     182     182     182     170     142     121     121     121
##   [34,]     178     181     182     182     177     155     140     127
##   [35,]     179     182     182     182     182     182     167     143
##   [36,]     182     182     182     182     182     182     182     152
##   [37,]     156     170     182     182     182     182     182     175
##   [38,]     136     152     156     178     182     182     182     182
##   [39,]     121     129     130     153     175     182     182     182
##   [40,]     121     121     121     129     152     165     182     182
##   [41,]     121     121     121     121     129     133     147     163
##   [42,]     121     121     121     121     121     121     121     137
##   [43,]     121     121     121     121     121     121     121     121
##   [44,]     121     121     121     121     121     121     121     121
##   [45,]     121     121     121     121     121     121     121     121
##   [46,]     121     121     121     121     121     121     121     121
##   [47,]     121     121     121     121     121     121     121     121
##   [48,]     121     121     121     121     121     121     121     121
##   [49,]     121     121     121     121     121     121     121     121
##   [50,]     121     121     121     121     121     121     121     121
##   [51,]     121     121     121     121     121     121     121     121
##   [52,]     121     121     121     121     121     121     121     121
##   [53,]     121     121     121     121     121     121     121     121
##   [54,]     126     124     122     121     121     121     121     121
##   [55,]     135     131     124     121     121     121     121     121
##   [56,]     148     141     127     121     121     121     121     121
##   [57,]     182     163     140     121     121     121     121     141
##   [58,]     179     182     153     138     121     121     145     156
##   [59,]     184     176     170     170     151     140     153     166
##   [60,]     196     188     182     182     182     173     169     168
##   [61,]     214     225     203     186     182     181     176     171
##   [62,]     231     243     215     182     183     178     171     164
##   [63,]     240     242     222     202     188     183     178     167
##   [64,]     241     242     233     206     194     187     183     182
##   [65,]     242     240     243     207     193     185     183     174
##   [66,]     243     207     182     182     182     179     171     161
##   [67,]     192     186     189     182     182     172     164     155
##   [68,]     182     185     183     183     175     161     151     141
##   [69,]     195     182     180     171     162     147     135     126
##   [70,]     185     182     175     163     151     128     123     122
##   [71,]     193     182     182     169     162     151     121     121
##   [72,]     218     214     206     195     191     186     171     167
##   [73,]     241     243     243     226     216     204     191     181
##   [74,]     267     289     269     256     237     223     203     185
##   [75,]     304     297     304     304     259     243     196     184
##   [76,]     303     304     284     255     259     243     205     182
##   [77,]     275     243     243     243     243     243     216     182
##   [78,]     259     248     244     243     243     243     221     182
##   [79,]     283     254     244     244     243     243     201     187
##   [80,]     292     282     263     243     243     228     198     188
##   [81,]     318     309     294     276     255     243     213     196
##   [82,]     349     332     313     304     270     243     229     227
##   [83,]     365     356     326     309     294     260     242     238
##         [,1065] [,1066] [,1067] [,1068] [,1069] [,1070] [,1071] [,1072]
##    [1,]      37      36      36      36      37      37      38      38
##    [2,]      39      39      39      39      39      39      38      38
##    [3,]      41      42      42      41      40      40      39      39
##    [4,]      45      46      44      43      43      42      42      42
##    [5,]      48      49      47      47      47      46      46      45
##    [6,]      51      52      51      50      50      49      49      48
##    [7,]      55      55      54      53      54      53      51      50
##    [8,]      58      57      57      57      57      56      54      53
##    [9,]      60      60      59      60      60      59      57      56
##   [10,]      60      60      60      60      60      60      59      59
##   [11,]      61      61      61      61      61      61      60      60
##   [12,]      65      63      64      64      63      62      60      62
##   [13,]      68      66      67      66      66      65      65      64
##   [14,]      70      67      68      68      68      68      69      67
##   [15,]      72      69      71      71      71      72      72      71
##   [16,]      73      71      74      74      74      76      76      75
##   [17,]      73      73      77      77      79      83      85      83
##   [18,]      74      75      80      83      89      97     103      96
##   [19,]      67      74      82      90     103     116     121     110
##   [20,]      60      60      77      90     112     121     115     115
##   [21,]      60      63      64      76      94     106     113     117
##   [22,]      60      60      60      66      87      94     103     111
##   [23,]      60      60      60      60      79      87      97     107
##   [24,]      60      60      60      60      68      78      90     102
##   [25,]      60      60      60      60      60      69      87     103
##   [26,]      60      60      60      60      60      60      89     116
##   [27,]      60      60      60      60      60      82      95     121
##   [28,]      60      60      60      60      68      86     104     117
##   [29,]      76      60      60      60      75      93     107     114
##   [30,]      99      88      68      66      84      99     110     115
##   [31,]     121     121      89      86      95     104     111     114
##   [32,]     121     121     102      99     104     107     111     113
##   [33,]     121     121     111     112     114     113     113     114
##   [34,]     121     121     120     121     121     118     117     117
##   [35,]     123     121     121     123     123     121     120     120
##   [36,]     121     123     121     129     128     124     121     121
##   [37,]     147     121     139     143     137     130     124     121
##   [38,]     167     170     172     163     148     135     126     123
##   [39,]     182     182     180     182     156     137     124     121
##   [40,]     182     182     182     160     150     134     127     122
##   [41,]     172     174     166     146     135     127     124     122
##   [42,]     147     149     145     131     125     123     122     122
##   [43,]     128     129     129     122     121     121     121     121
##   [44,]     121     122     123     121     118     117     118     121
##   [45,]     121     121     121     118     115     114     114     117
##   [46,]     121     121     121     115     110     108     106     107
##   [47,]     121     121     117     111     106     101      98      96
##   [48,]     121     121     115     107     100      94      88      82
##   [49,]     121     121     112     103      95      87      78      68
##   [50,]     121     121     111     102      93      84      75      63
##   [51,]     121     121     111     103      94      87      80      70
##   [52,]     121     121     112     105      98      93      88      78
##   [53,]     121     121     113     108     104     101      96      86
##   [54,]     121     121     116     113     112     111     103      92
##   [55,]     121     121     121     120     121     121     112      99
##   [56,]     121     121     121     121     124     122     121     107
##   [57,]     158     136     135     134     130     125     122     110
##   [58,]     182     170     167     159     140     130     121     111
##   [59,]     176     182     182     182     158     140     127     117
##   [60,]     178     181     182     182     163     151     139     121
##   [61,]     166     167     162     170     165     160     160     169
##   [62,]     150     134     121     141     145     158     171     182
##   [63,]     146     121     123     122     121     132     160     170
##   [64,]     153     121     121     121     121     121     129     142
##   [65,]     145     132     124     121     121     121     121     128
##   [66,]     142     134     128     124     121     121     121     121
##   [67,]     143     134     128     123     121     121     121     121
##   [68,]     133     126     123     122     121     121     121     121
##   [69,]     121     123     122     121     121     121     121     121
##   [70,]     122     121     122     121     121     122     121     121
##   [71,]     121     121     132     129     126     122     121     121
##   [72,]     179     170     151     139     131     123     121     121
##   [73,]     182     182     167     149     133     122     121     121
##   [74,]     182     179     169     153     137     125     121     121
##   [75,]     182     182     175     155     138     124     122     121
##   [76,]     183     182     182     151     132     122     121     121
##   [77,]     183     163     153     131     125     122     140     154
##   [78,]     183     165     146     121     121     152     182     182
##   [79,]     184     171     160     149     144     172     182     165
##   [80,]     184     183     179     175     174     175     155     142
##   [81,]     194     198     193     188     183     169     144     121
##   [82,]     230     243     225     204     186     166     149     135
##   [83,]     241     242     243     218     190     172     159     145
##         [,1073] [,1074] [,1075] [,1076] [,1077] [,1078] [,1079] [,1080]
##    [1,]      38      38      37      37      36      36      36      36
##    [2,]      38      38      38      38      38      38      38      39
##    [3,]      39      39      39      39      39      39      41      43
##    [4,]      42      42      42      42      41      41      43      44
##    [5,]      45      45      45      44      43      43      45      46
##    [6,]      48      48      47      47      45      45      46      48
##    [7,]      51      51      50      49      47      47      48      49
##    [8,]      53      53      53      51      49      48      49      50
##    [9,]      56      56      55      53      50      50      51      51
##   [10,]      59      59      58      55      52      51      52      53
##   [11,]      61      60      59      57      54      53      53      54
##   [12,]      62      61      60      59      55      53      54      55
##   [13,]      63      62      61      59      56      55      56      56
##   [14,]      66      64      63      61      58      57      57      57
##   [15,]      69      67      65      62      60      58      58      58
##   [16,]      73      71      68      62      60      60      60      60
##   [17,]      80      78      74      66      60      60      60      62
##   [18,]      92      88      81      71      68      65      67      66
##   [19,]     104     100      92      78      75      73      72      70
##   [20,]     115     113     103      85      81      79      78      75
##   [21,]     121     121     107      92      88      83      81      78
##   [22,]     115     119     107      98      94      89      87      83
##   [23,]     113     118     110     103      99      95      92      88
##   [24,]     111     118     117     110     105     101      97      93
##   [25,]     113     121     121     117     111     107     104     100
##   [26,]     117     119     121     121     119     116     116     109
##   [27,]     121     121     121     121     121     121     121     121
##   [28,]     121     121     121     121     121     121     121     119
##   [29,]     117     120     121     121     121     121     121     121
##   [30,]     117     118     120     121     121     121     121     121
##   [31,]     116     118     120     121     121     121     121     121
##   [32,]     115     118     120     121     121     121     121     121
##   [33,]     116     118     120     121     121     121     121     121
##   [34,]     117     119     121     121     121     121     121     121
##   [35,]     119     120     121     121     121     121     121     121
##   [36,]     121     121     121     121     121     121     121     121
##   [37,]     121     121     121     121     121     121     121     120
##   [38,]     121     121     121     121     121     121     121     120
##   [39,]     121     121     121     121     121     121     121     119
##   [40,]     121     121     121     121     121     121     121     116
##   [41,]     122     121     121     121     121     121     121     108
##   [42,]     121     121     121     121     121     121     111      99
##   [43,]     121     121     121     121     121     121     110      95
##   [44,]     121     121     121     121     121     121     114      98
##   [45,]     121     121     121     121     121     121     117      97
##   [46,]     114     121     121     121     121     121     117     100
##   [47,]      98     102     111     121     111     121      97      89
##   [48,]      80      80      81      80      76      72      73      75
##   [49,]      60      60      60      60      63      60      60      60
##   [50,]      61      60      60      60      60      60      60      60
##   [51,]      60      60      60      60      60      60      60      60
##   [52,]      71      68      67      66      64      62      61      60
##   [53,]      78      75      73      71      69      66      63      60
##   [54,]      82      79      77      74      72      69      65      60
##   [55,]      88      86      83      79      76      72      67      63
##   [56,]      95      92      88      85      81      75      70      66
##   [57,]     101      98      94      90      86      80      74      70
##   [58,]     107     104     100      96      92      85      79      74
##   [59,]     114     110     106     102      97      91      84      79
##   [60,]     121     117     112     107     103      96      88      83
##   [61,]     147     127     119     113     110     102      93      87
##   [62,]     182     141     128     121     121     110      99      94
##   [63,]     145     137     128     123     122     119     106     101
##   [64,]     141     133     125     121     121     121     117     116
##   [65,]     130     128     121     121     121     121     121     121
##   [66,]     122     122     122     121     121     121     121     121
##   [67,]     121     121     121     121     121     121     121     121
##   [68,]     121     121     121     121     121     121     121     121
##   [69,]     121     121     121     121     121     121     121     121
##   [70,]     121     121     121     121     121     121     121     121
##   [71,]     121     121     121     121     121     121     121     121
##   [72,]     121     121     121     121     121     121     121     120
##   [73,]     121     121     121     121     121     121     120     119
##   [74,]     121     121     121     121     121     121     120     119
##   [75,]     121     124     122     122     121     120     119     118
##   [76,]     130     126     123     122     121     120     118     116
##   [77,]     139     129     124     122     120     119     117     115
##   [78,]     145     128     121     122     120     119     116     113
##   [79,]     131     124     123     122     119     118     115     112
##   [80,]     121     122     123     122     121     121     117     113
##   [81,]     126     123     121     134     133     130     124     119
##   [82,]     121     121     151     172     160     148     135     121
##   [83,]     140     153     172     196     189     174     159     140
##         [,1081] [,1082] [,1083] [,1084] [,1085] [,1086] [,1087] [,1088]
##    [1,]      36      35      35      36      38      41      44      47
##    [2,]      39      40      41      42      44      46      48      50
##    [3,]      43      44      45      47      48      50      51      53
##    [4,]      45      45      47      49      50      51      52      54
##    [5,]      46      47      48      50      51      52      53      54
##    [6,]      48      48      49      51      52      53      54      55
##    [7,]      49      49      50      52      53      53      54      56
##    [8,]      51      50      51      52      53      54      55      56
##    [9,]      52      52      52      53      54      55      56      57
##   [10,]      53      53      53      54      55      56      57      57
##   [11,]      54      54      54      55      56      57      58      58
##   [12,]      55      55      55      56      57      58      58      59
##   [13,]      56      56      56      57      58      58      59      59
##   [14,]      58      57      57      58      59      59      59      60
##   [15,]      59      58      58      59      59      59      59      60
##   [16,]      60      59      59      59      59      59      60      60
##   [17,]      62      61      60      60      60      60      60      60
##   [18,]      65      62      60      60      60      60      60      60
##   [19,]      68      64      61      60      60      60      60      60
##   [20,]      72      67      63      61      60      60      60      60
##   [21,]      75      70      66      64      61      60      60      60
##   [22,]      80      74      69      66      63      61      61      60
##   [23,]      84      78      72      68      65      62      60      60
##   [24,]      88      81      75      70      65      61      61      60
##   [25,]      91      83      78      72      66      62      60      60
##   [26,]      98      89      82      74      67      60      60      60
##   [27,]     106      97      89      79      70      60      60      60
##   [28,]     116     114     102      89      77      66      60      72
##   [29,]     121     121     121     101      90      81      84      89
##   [30,]     121     121     119     110     103      98      96     102
##   [31,]     121     121     121     119     117     117     113     117
##   [32,]     121     121     121     121     121     120     121     121
##   [33,]     121     121     121     121     121     121     121     121
##   [34,]     121     121     121     121     121     121     121     121
##   [35,]     121     121     121     121     121     121     121     121
##   [36,]     121     120     119     120     121     121     120     121
##   [37,]     119     118     117     117     117     117     119     121
##   [38,]     118     116     114     113     114     115     118     121
##   [39,]     116     113     111     109     110     112     118     121
##   [40,]     111     107     103      99     102     107     119     121
##   [41,]      97      90      83      86      93     101     121     121
##   [42,]      83      71      60      62      69      72      92     112
##   [43,]      77      60      62      60      61      60      60      81
##   [44,]      80      70      60      60      60      60      60      60
##   [45,]      84      72      60      60      60      60      60      60
##   [46,]      87      75      67      60      60      60      60      60
##   [47,]      84      76      68      60      60      60      60      60
##   [48,]      73      70      66      60      60      60      60      60
##   [49,]      60      60      62      62      60      60      60      60
##   [50,]      60      60      60      61      61      60      60      60
##   [51,]      60      60      60      60      60      60      60      60
##   [52,]      60      60      60      60      60      60      60      60
##   [53,]      60      60      60      60      60      60      60      60
##   [54,]      60      60      60      60      60      60      60      60
##   [55,]      60      60      60      60      60      60      60      60
##   [56,]      63      60      60      60      60      60      60      60
##   [57,]      66      62      60      60      60      60      60      60
##   [58,]      70      66      63      60      60      60      60      60
##   [59,]      74      69      65      63      61      60      60      60
##   [60,]      78      73      67      63      60      60      60      60
##   [61,]      81      75      68      61      60      60      60      60
##   [62,]      87      79      69      60      60      60      60      60
##   [63,]      93      84      72      63      60      60      60      60
##   [64,]     105      94      76      63      61      60      60      60
##   [65,]     121     104      72      61      60      60      60      60
##   [66,]     121     107      60      61      61      66      71      68
##   [67,]     121      95      79      60      74      79      84      80
##   [68,]     121     102      89      85      88      94      98      92
##   [69,]     121     113     102     101     103     107     112     104
##   [70,]     121     121     116     117     115     118     120     117
##   [71,]     121     121     121     121     121     121     121     121
##   [72,]     120     121     121     121     121     121     121     121
##   [73,]     119     119     119     121     121     121     121     121
##   [74,]     118     118     117     119     119     121     121     121
##   [75,]     116     115     115     116     117     118     121     121
##   [76,]     114     113     112     113     113     113     116     121
##   [77,]     112     110     108     108     106     105     106     110
##   [78,]     110     107     103     101      98      95      93      96
##   [79,]     108     104      98      93      89      84      80      76
##   [80,]     108     103      95      87      82      76      70      60
##   [81,]     112     106      98      89      82      76      69      63
##   [82,]     118     109      99      92      85      78      71      65
##   [83,]     126     116     104      95      87      79      71      65
##         [,1089] [,1090] [,1091] [,1092] [,1093] [,1094] [,1095] [,1096]
##    [1,]      50      53      56      58      59      60      61      62
##    [2,]      52      55      58      60      61      61      61      62
##    [3,]      55      57      60      61      62      62      62      62
##    [4,]      55      57      60      61      61      62      61      61
##    [5,]      56      57      60      60      60      60      60      60
##    [6,]      56      58      60      60      60      60      60      60
##    [7,]      56      58      60      60      60      60      60      60
##    [8,]      57      58      60      60      60      60      60      60
##    [9,]      58      60      60      60      60      60      60      60
##   [10,]      59      60      60      60      60      60      60      60
##   [11,]      59      60      60      60      60      60      60      60
##   [12,]      60      60      60      60      60      60      60      60
##   [13,]      60      60      60      60      60      60      60      60
##   [14,]      60      60      60      60      60      60      60      60
##   [15,]      60      60      60      60      60      60      60      60
##   [16,]      60      60      60      60      60      60      60      60
##   [17,]      60      60      60      60      60      60      60      60
##   [18,]      60      60      60      60      60      60      60      60
##   [19,]      60      60      60      60      60      60      60      60
##   [20,]      60      60      60      60      60      60      60      60
##   [21,]      60      60      60      60      60      60      60      60
##   [22,]      60      60      60      60      60      60      60      60
##   [23,]      60      60      60      60      60      60      60      60
##   [24,]      60      60      60      60      60      60      60      60
##   [25,]      60      60      60      60      60      60      60      60
##   [26,]      60      60      60      60      60      60      60      60
##   [27,]      65      64      61      60      60      60      60      60
##   [28,]      73      69      64      60      61      60      60      60
##   [29,]      85      78      70      67      62      61      60      60
##   [30,]      93      84      75      69      64      61      60      60
##   [31,]     103      92      80      71      64      61      60      60
##   [32,]     110      97      82      67      60      61      60      60
##   [33,]     117     104      83      67      63      61      60      60
##   [34,]     121     121      89      77      70      63      60      60
##   [35,]     121     106      93      81      72      64      61      60
##   [36,]     121     110      98      85      70      60      60      60
##   [37,]     121     110      99      87      70      61      61      60
##   [38,]     121     110     100      91      74      65      60      60
##   [39,]     121     113     105      97      77      68      64      60
##   [40,]     121     117     110     104      80      70      66      64
##   [41,]     121     121     116     110      82      72      68      66
##   [42,]     121     121     121     118      84      74      70      68
##   [43,]     103     121     111      98      86      76      71      69
##   [44,]      80      88      93      92      85      77      72      69
##   [45,]      60      71      75      76      76      72      68      67
##   [46,]      60      60      63      65      66      63      60      62
##   [47,]      60      60      60      61      61      60      60      60
##   [48,]      60      60      60      60      60      60      60      60
##   [49,]      60      60      60      60      60      60      60      60
##   [50,]      60      60      60      60      60      60      60      60
##   [51,]      60      60      60      60      60      60      60      60
##   [52,]      60      60      60      60      60      60      60      60
##   [53,]      60      60      60      60      60      60      60      60
##   [54,]      60      60      60      60      60      60      60      60
##   [55,]      60      60      60      60      60      60      60      60
##   [56,]      60      60      60      60      60      60      60      60
##   [57,]      60      60      60      60      60      60      60      60
##   [58,]      60      60      60      60      60      60      60      60
##   [59,]      60      60      60      60      60      60      60      60
##   [60,]      60      60      60      60      60      60      60      60
##   [61,]      60      60      60      60      60      60      60      60
##   [62,]      60      60      60      60      60      60      60      60
##   [63,]      60      60      60      60      60      60      60      60
##   [64,]      60      60      60      60      60      60      60      60
##   [65,]      60      60      60      60      60      60      60      60
##   [66,]      63      60      61      60      60      60      60      60
##   [67,]      74      66      60      60      60      60      60      60
##   [68,]      85      75      65      60      60      60      60      60
##   [69,]      96      84      72      65      60      60      60      60
##   [70,]     108      94      79      70      60      60      60      60
##   [71,]     121     105      88      78      69      60      60      60
##   [72,]     121     114      95      84      75      67      60      60
##   [73,]     121     118     105      94      83      74      65      60
##   [74,]     121     121     114     102      90      78      68      62
##   [75,]     121     121     121     106      92      79      67      61
##   [76,]     120     121     121     105      90      76      60      61
##   [77,]     116     121     121     101      87      74      68      61
##   [78,]     101     121     101      95      84      74      67      62
##   [79,]      71      82      86      84      79      73      67      61
##   [80,]      60      60      67      68      69      66      60      61
##   [81,]      60      60      60      62      62      62      62      61
##   [82,]      60      60      60      60      60      60      60      60
##   [83,]      61      60      60      60      60      60      60      60
##         [,1097] [,1098] [,1099] [,1100] [,1101] [,1102] [,1103] [,1104]
##    [1,]      62      63      62      60      57      53      48      44
##    [2,]      63      65      65      63      61      58      53      49
##    [3,]      64      66      66      65      63      61      57      53
##    [4,]      62      64      64      64      63      62      60      57
##    [5,]      60      61      61      61      61      60      60      59
##    [6,]      60      60      60      60      60      60      60      60
##    [7,]      60      60      60      60      60      60      60      60
##    [8,]      60      60      60      60      60      60      60      60
##    [9,]      60      60      60      60      60      60      60      60
##   [10,]      60      60      60      60      60      60      60      60
##   [11,]      60      60      60      60      60      60      60      60
##   [12,]      60      60      60      60      60      60      60      60
##   [13,]      60      60      60      60      60      60      60      60
##   [14,]      60      60      60      60      60      60      60      60
##   [15,]      60      60      60      60      60      60      60      60
##   [16,]      60      60      60      60      60      60      60      60
##   [17,]      60      60      60      60      60      60      60      60
##   [18,]      60      60      60      60      60      60      60      60
##   [19,]      60      60      60      60      60      60      60      60
##   [20,]      60      60      60      60      60      60      60      60
##   [21,]      60      60      60      60      60      60      60      60
##   [22,]      60      60      60      60      60      60      60      60
##   [23,]      60      60      60      60      60      60      60      60
##   [24,]      60      60      60      60      60      60      60      60
##   [25,]      60      60      60      60      60      60      60      60
##   [26,]      60      60      60      60      60      60      60      60
##   [27,]      60      60      60      60      60      60      60      60
##   [28,]      60      60      60      60      60      60      60      60
##   [29,]      60      60      60      60      60      60      60      60
##   [30,]      60      60      60      60      60      60      60      60
##   [31,]      60      60      60      60      60      60      60      60
##   [32,]      60      60      60      60      60      60      60      60
##   [33,]      60      60      60      60      60      60      60      60
##   [34,]      60      60      60      60      60      60      60      60
##   [35,]      60      60      60      60      60      60      60      60
##   [36,]      60      60      60      60      60      60      60      60
##   [37,]      60      60      60      60      60      60      60      60
##   [38,]      60      60      60      60      60      60      60      60
##   [39,]      60      60      60      60      60      60      60      60
##   [40,]      62      61      60      60      60      60      60      60
##   [41,]      64      62      61      60      60      60      60      60
##   [42,]      65      64      62      60      60      60      60      60
##   [43,]      66      64      62      60      60      60      60      60
##   [44,]      66      64      62      60      60      60      60      60
##   [45,]      65      64      61      60      60      60      60      60
##   [46,]      62      62      61      60      60      60      60      60
##   [47,]      60      60      60      60      60      60      60      60
##   [48,]      60      60      60      60      60      60      60      60
##   [49,]      60      60      60      60      60      60      60      60
##   [50,]      60      60      60      60      60      60      60      60
##   [51,]      60      60      60      60      60      60      60      60
##   [52,]      60      60      60      60      60      60      60      60
##   [53,]      60      60      60      60      60      60      60      60
##   [54,]      60      60      60      60      60      60      60      60
##   [55,]      60      60      60      60      60      60      60      60
##   [56,]      60      60      60      60      60      60      60      60
##   [57,]      60      60      60      60      60      60      60      60
##   [58,]      60      60      60      60      60      60      60      60
##   [59,]      60      60      60      60      60      60      60      60
##   [60,]      60      60      60      60      60      60      60      60
##   [61,]      60      60      60      60      60      60      60      60
##   [62,]      60      60      60      60      60      60      60      60
##   [63,]      60      60      60      60      60      60      60      60
##   [64,]      60      60      60      60      60      60      60      60
##   [65,]      60      60      60      60      60      60      60      60
##   [66,]      60      60      60      60      60      60      60      60
##   [67,]      60      60      60      60      60      60      60      60
##   [68,]      60      60      60      60      60      60      60      60
##   [69,]      60      60      60      60      60      60      60      60
##   [70,]      60      60      60      60      60      60      60      60
##   [71,]      60      60      60      60      60      60      60      60
##   [72,]      60      60      60      60      60      60      60      60
##   [73,]      60      60      60      60      60      60      60      60
##   [74,]      60      60      60      60      60      60      60      60
##   [75,]      60      60      60      60      60      60      60      60
##   [76,]      60      60      60      60      60      60      60      60
##   [77,]      60      60      60      60      60      60      60      60
##   [78,]      60      60      60      60      60      60      60      60
##   [79,]      60      60      60      60      60      60      60      60
##   [80,]      60      60      60      60      60      60      60      60
##   [81,]      60      60      60      60      60      60      60      60
##   [82,]      60      60      60      60      60      60      60      60
##   [83,]      60      60      60      60      60      60      60      60
##         [,1105] [,1106] [,1107] [,1108] [,1109] [,1110] [,1111] [,1112]
##    [1,]      40      36      34      32      29      27      24      22
##    [2,]      45      41      39      36      34      31      27      25
##    [3,]      49      45      42      40      37      33      29      26
##    [4,]      54      50      47      44      41      37      31      27
##    [5,]      58      55      52      49      45      40      33      28
##    [6,]      60      58      55      52      48      42      34      28
##    [7,]      60      60      58      55      50      43      35      29
##    [8,]      60      60      59      56      50      42      34      27
##    [9,]      60      60      60      57      50      42      33      26
##   [10,]      60      60      60      57      50      42      33      26
##   [11,]      60      60      60      57      50      42      33      26
##   [12,]      60      60      60      59      51      42      33      24
##   [13,]      60      60      60      59      51      42      33      24
##   [14,]      60      60      60      59      51      42      33      24
##   [15,]      60      60      60      60      52      42      33      24
##   [16,]      60      60      60      59      51      42      33      24
##   [17,]      60      60      60      59      51      42      33      24
##   [18,]      60      60      60      57      50      42      33      25
##   [19,]      60      60      60      57      50      42      34      25
##   [20,]      60      60      60      57      50      42      34      25
##   [21,]      60      60      60      57      50      42      34      26
##   [22,]      60      60      60      60      51      43      34      26
##   [23,]      60      60      60      60      52      43      35      26
##   [24,]      60      60      60      60      52      43      35      26
##   [25,]      60      60      60      60      52      44      35      27
##   [26,]      60      60      60      60      52      44      36      27
##   [27,]      60      60      60      60      52      44      36      27
##   [28,]      60      60      60      60      53      45      36      28
##   [29,]      60      60      60      60      53      45      37      28
##   [30,]      60      60      60      60      54      46      37      28
##   [31,]      60      60      60      60      55      46      37      29
##   [32,]      60      60      60      60      56      47      38      29
##   [33,]      60      60      60      60      57      47      38      29
##   [34,]      60      60      60      60      58      47      39      29
##   [35,]      60      60      60      60      60      47      39      30
##   [36,]      60      60      60      60      52      47      39      30
##   [37,]      60      60      60      60      52      47      39      30
##   [38,]      60      60      60      60      53      47      40      30
##   [39,]      60      60      60      60      53      48      40      31
##   [40,]      60      60      60      60      53      49      40      31
##   [41,]      60      60      60      60      54      50      41      31
##   [42,]      60      60      60      60      54      51      41      31
##   [43,]      60      60      60      60      55      52      41      32
##   [44,]      60      60      60      60      55      53      42      29
##   [45,]      60      60      60      60      56      54      42      29
##   [46,]      60      60      60      60      57      55      42      30
##   [47,]      60      60      60      60      58      57      42      30
##   [48,]      60      60      60      60      59      58      42      30
##   [49,]      60      60      60      60      60      59      41      31
##   [50,]      60      60      60      60      60      60      41      31
##   [51,]      60      60      60      60      60      49      40      31
##   [52,]      60      60      60      60      60      49      40      32
##   [53,]      60      60      60      60      60      49      38      32
##   [54,]      60      60      60      60      60      49      37      31
##   [55,]      60      60      60      60      60      50      38      32
##   [56,]      60      60      60      60      60      50      38      32
##   [57,]      60      60      60      60      60      50      39      33
##   [58,]      60      60      60      60      60      50      37      33
##   [59,]      60      60      60      60      60      50      39      34
##   [60,]      60      60      60      60      60      50      39      34
##   [61,]      60      60      60      60      60      50      39      35
##   [62,]      60      60      60      60      60      50      40      35
##   [63,]      60      60      60      60      60      50      40      36
##   [64,]      60      60      60      60      60      46      38      37
##   [65,]      60      60      60      60      60      47      39      37
##   [66,]      60      60      60      60      60      47      39      38
##   [67,]      60      60      60      60      60      47      40      38
##   [68,]      60      60      60      60      60      47      40      39
##   [69,]      60      60      60      60      60      47      41      39
##   [70,]      60      60      60      60      60      48      41      40
##   [71,]      60      60      60      60      60      48      42      40
##   [72,]      60      60      60      60      60      48      42      41
##   [73,]      60      60      60      60      60      48      43      42
##   [74,]      60      60      60      60      56      46      43      42
##   [75,]      60      60      60      60      56      46      44      43
##   [76,]      60      60      60      60      56      47      44      43
##   [77,]      60      60      60      60      56      47      45      44
##   [78,]      60      60      60      60      56      48      46      45
##   [79,]      60      60      60      60      56      48      46      45
##   [80,]      60      60      60      60      56      48      46      46
##   [81,]      60      60      60      60      56      49      47      46
##   [82,]      60      60      60      60      56      49      47      47
##   [83,]      60      60      60      60      56      50      48      47
##         [,1113] [,1114] [,1115] [,1116] [,1117] [,1118] [,1119] [,1120]
##    [1,]      20      19      18      17      17      17      17      18
##    [2,]      23      22      21      21      21      21      22      23
##    [3,]      25      24      24      24      24      25      26      27
##    [4,]      25      23      23      24      25      25      26      28
##    [5,]      24      22      22      24      25      25      26      29
##    [6,]      24      22      22      24      25      26      27      29
##    [7,]      24      22      22      25      26      26      27      29
##    [8,]      23      22      22      25      26      26      27      30
##    [9,]      22      21      22      25      26      27      28      30
##   [10,]      22      21      23      26      27      27      28      30
##   [11,]      21      21      23      26      27      27      28      31
##   [12,]      21      22      25      27      28      28      29      31
##   [13,]      21      23      26      28      28      28      29      31
##   [14,]      21      23      27      28      28      28      29      32
##   [15,]      21      23      27      28      29      29      30      32
##   [16,]      22      24      27      29      29      29      30      32
##   [17,]      22      24      28      29      29      29      30      32
##   [18,]      22      24      28      30      30      30      31      33
##   [19,]      23      25      28      30      30      30      31      33
##   [20,]      23      25      29      30      30      30      31      33
##   [21,]      22      25      29      31      31      31      31      34
##   [22,]      18      25      30      31      31      31      31      34
##   [23,]      18      28      31      32      32      32      32      35
##   [24,]      18      28      31      32      32      32      32      35
##   [25,]      19      28      32      32      32      32      32      35
##   [26,]      19      29      32      32      32      32      32      35
##   [27,]      19      29      32      33      33      33      33      36
##   [28,]      20      29      33      33      33      33      33      36
##   [29,]      20      30      33      33      33      33      33      37
##   [30,]      21      30      33      34      34      34      34      37
##   [31,]      21      31      34      34      34      34      34      37
##   [32,]      21      31      34      35      35      35      34      38
##   [33,]      24      32      35      35      35      35      35      38
##   [34,]      26      34      35      35      35      35      35      38
##   [35,]      27      34      35      35      35      35      35      39
##   [36,]      27      35      36      36      36      36      36      39
##   [37,]      27      35      36      36      36      36      36      39
##   [38,]      28      35      36      37      37      36      36      40
##   [39,]      28      36      37      37      37      37      38      40
##   [40,]      29      36      37      37      37      37      38      40
##   [41,]      29      37      37      38      38      37      39      41
##   [42,]      30      37      38      38      38      38      39      41
##   [43,]      30      37      38      38      38      38      39      42
##   [44,]      35      38      39      39      39      38      40      42
##   [45,]      35      38      39      39      39      39      40      42
##   [46,]      36      39      39      39      39      39      40      42
##   [47,]      36      39      39      40      39      39      40      42
##   [48,]      37      39      40      40      40      40      41      43
##   [49,]      37      40      40      40      40      40      41      43
##   [50,]      38      40      41      41      40      40      43      43
##   [51,]      38      40      41      41      41      41      43      44
##   [52,]      39      41      41      41      41      41      43      44
##   [53,]      39      41      42      42      42      41      44      44
##   [54,]      39      42      42      42      42      42      44      45
##   [55,]      40      42      42      42      42      42      44      45
##   [56,]      40      42      43      43      42      42      45      45
##   [57,]      41      43      43      43      43      43      45      45
##   [58,]      41      43      43      43      43      43      45      46
##   [59,]      42      43      44      44      43      43      45      46
##   [60,]      42      44      44      44      44      44      46      46
##   [61,]      42      44      44      44      44      44      46      46
##   [62,]      43      44      45      45      44      44      46      47
##   [63,]      43      45      45      45      45      45      46      47
##   [64,]      44      45      45      45      45      45      47      47
##   [65,]      44      46      46      46      46      45      47      47
##   [66,]      45      46      46      46      46      46      48      48
##   [67,]      45      46      46      46      46      46      48      48
##   [68,]      46      47      47      47      46      46      48      48
##   [69,]      46      47      47      47      47      47      48      49
##   [70,]      46      47      47      47      47      47      49      49
##   [71,]      47      48      48      48      47      47      49      49
##   [72,]      47      48      48      48      48      48      49      49
##   [73,]      48      48      48      48      48      48      49      50
##   [74,]      48      49      49      49      48      48      50      50
##   [75,]      48      49      49      49      49      49      50      50
##   [76,]      49      49      49      49      49      49      50      50
##   [77,]      49      50      50      50      49      49      50      51
##   [78,]      50      50      50      50      50      49      51      51
##   [79,]      50      50      50      50      50      50      51      51
##   [80,]      50      51      51      51      50      50      51      51
##   [81,]      51      51      51      51      51      50      52      52
##   [82,]      51      52      51      51      51      51      52      52
##   [83,]      52      52      52      52      51      51      52      52
##         [,1121] [,1122] [,1123] [,1124] [,1125] [,1126] [,1127] [,1128]
##    [1,]      19      20      21      22      23      24      25      26
##    [2,]      24      26      28      29      30      31      33      34
##    [3,]      29      31      33      34      36      37      39      41
##    [4,]      30      33      35      37      38      40      42      44
##    [5,]      31      34      36      37      38      41      42      44
##    [6,]      31      34      37      38      39      41      42      44
##    [7,]      31      35      37      38      39      41      43      45
##    [8,]      32      35      37      38      39      41      43      45
##    [9,]      32      36      38      38      39      42      43      45
##   [10,]      32      36      38      39      39      42      43      45
##   [11,]      33      37      38      39      39      42      44      45
##   [12,]      33      37      39      39      39      42      44      44
##   [13,]      33      37      39      39      39      42      44      45
##   [14,]      34      37      39      39      39      42      44      45
##   [15,]      34      38      39      39      39      43      44      47
##   [16,]      34      38      39      40      40      43      44      47
##   [17,]      34      38      40      40      40      43      45      47
##   [18,]      35      39      40      40      40      43      45      47
##   [19,]      36      39      40      40      40      43      45      47
##   [20,]      37      40      40      41      41      44      45      47
##   [21,]      37      40      41      41      41      44      45      48
##   [22,]      37      40      41      41      41      44      46      47
##   [23,]      37      41      41      41      41      44      46      48
##   [24,]      38      41      41      41      41      44      46      48
##   [25,]      38      41      41      42      42      45      46      48
##   [26,]      38      41      42      42      42      45      46      50
##   [27,]      39      41      42      42      42      45      47      50
##   [28,]      39      42      42      42      42      45      47      50
##   [29,]      40      42      42      42      42      45      47      50
##   [30,]      41      42      42      43      43      46      47      50
##   [31,]      41      42      43      43      43      46      47      50
##   [32,]      42      42      43      43      43      46      47      50
##   [33,]      42      43      43      43      43      46      48      50
##   [34,]      42      43      43      43      43      46      48      51
##   [35,]      42      43      43      44      44      47      48      51
##   [36,]      42      43      44      44      44      47      48      51
##   [37,]      43      44      44      44      44      47      48      51
##   [38,]      43      44      44      44      44      48      48      51
##   [39,]      43      44      44      45      45      48      49      51
##   [40,]      43      44      45      45      45      48      49      51
##   [41,]      44      45      45      45      45      48      49      52
##   [42,]      44      45      45      45      45      48      49      52
##   [43,]      44      45      45      45      45      48      49      52
##   [44,]      44      45      46      46      46      48      49      52
##   [45,]      45      46      46      46      47      49      49      52
##   [46,]      45      46      46      46      47      49      49      52
##   [47,]      45      46      46      46      47      49      49      52
##   [48,]      45      46      46      46      48      49      50      52
##   [49,]      46      46      46      46      48      50      50      52
##   [50,]      46      46      47      47      48      50      50      53
##   [51,]      46      47      47      47      48      50      50      53
##   [52,]      46      47      47      47      48      50      50      53
##   [53,]      47      47      47      47      49      50      50      53
##   [54,]      47      47      48      48      49      50      51      53
##   [55,]      47      48      48      48      50      51      51      53
##   [56,]      47      48      48      48      50      51      51      53
##   [57,]      47      48      48      48      50      51      51      53
##   [58,]      48      48      48      48      51      51      51      53
##   [59,]      48      49      49      49      51      51      51      53
##   [60,]      48      49      49      49      51      51      51      53
##   [61,]      49      49      49      49      51      52      52      54
##   [62,]      49      49      49      49      51      52      52      54
##   [63,]      49      49      49      49      51      52      52      54
##   [64,]      49      49      50      50      52      52      52      54
##   [65,]      49      50      50      50      52      52      52      54
##   [66,]      49      50      50      50      52      52      52      54
##   [67,]      50      50      50      50      52      52      52      54
##   [68,]      50      50      50      50      52      53      53      54
##   [69,]      50      51      51      51      52      53      53      54
##   [70,]      50      51      51      51      53      53      53      55
##   [71,]      51      51      51      51      53      53      53      55
##   [72,]      51      51      51      51      53      53      53      55
##   [73,]      51      51      51      51      53      53      53      55
##   [74,]      51      52      52      52      53      53      53      55
##   [75,]      52      52      52      52      53      53      53      55
##   [76,]      52      52      52      52      53      54      54      55
##   [77,]      52      52      52      52      53      54      54      55
##   [78,]      52      52      52      52      54      54      54      55
##   [79,]      53      53      53      53      54      54      54      55
##   [80,]      53      53      53      53      54      54      54      56
##   [81,]      53      53      53      53      54      54      54      56
##   [82,]      53      53      53      53      54      55      55      56
##   [83,]      53      53      53      53      55      55      55      56
##         [,1129] [,1130] [,1131] [,1132] [,1133] [,1134] [,1135] [,1136]
##    [1,]      27      28      29      29      29      29      30      30
##    [2,]      36      37      38      38      38      38      38      38
##    [3,]      43      44      45      45      45      45      45      45
##    [4,]      46      48      49      49      48      48      49      49
##    [5,]      47      49      50      50      48      49      49      50
##    [6,]      48      49      50      50      48      49      49      50
##    [7,]      48      50      50      50      48      49      49      50
##    [8,]      48      50      50      50      48      49      49      50
##    [9,]      48      50      50      50      48      49      50      50
##   [10,]      48      50      50      50      48      49      50      50
##   [11,]      48      50      50      50      48      49      50      50
##   [12,]      49      50      50      50      47      49      50      50
##   [13,]      49      50      50      51      47      49      50      51
##   [14,]      49      50      51      51      48      49      50      51
##   [15,]      50      50      51      51      48      49      50      51
##   [16,]      50      51      51      51      48      49      51      51
##   [17,]      50      51      51      51      48      49      51      51
##   [18,]      50      51      51      51      48      50      51      51
##   [19,]      50      51      51      51      48      50      51      51
##   [20,]      50      51      51      51      48      50      51      51
##   [21,]      50      51      51      51      48      50      51      51
##   [22,]      50      51      51      51      48      50      51      51
##   [23,]      51      51      51      51      48      51      51      51
##   [24,]      51      51      51      51      49      51      51      51
##   [25,]      51      51      51      52      49      51      51      52
##   [26,]      51      51      52      52      49      51      52      52
##   [27,]      51      52      52      52      49      51      52      52
##   [28,]      51      52      52      52      49      51      52      52
##   [29,]      51      52      52      52      49      51      52      52
##   [30,]      51      52      52      52      49      51      52      52
##   [31,]      51      52      52      52      50      52      52      52
##   [32,]      52      52      52      52      50      52      52      52
##   [33,]      52      52      52      52      50      52      52      52
##   [34,]      52      52      52      52      50      52      52      52
##   [35,]      52      52      52      52      50      52      52      52
##   [36,]      52      52      52      52      50      52      52      53
##   [37,]      52      52      52      53      51      52      53      53
##   [38,]      52      52      53      53      51      52      53      53
##   [39,]      52      53      53      53      51      53      53      53
##   [40,]      52      53      53      52      51      53      53      53
##   [41,]      53      53      53      51      52      53      53      53
##   [42,]      53      53      53      51      52      53      53      53
##   [43,]      53      53      53      52      52      53      53      53
##   [44,]      53      53      53      52      52      53      53      53
##   [45,]      53      53      53      52      52      53      53      53
##   [46,]      53      53      53      52      53      53      53      53
##   [47,]      53      53      53      52      53      53      53      53
##   [48,]      53      53      53      52      53      53      53      53
##   [49,]      53      53      53      52      53      53      53      53
##   [50,]      53      53      53      52      53      53      53      53
##   [51,]      53      53      53      51      53      53      53      54
##   [52,]      53      53      53      51      53      53      54      54
##   [53,]      53      53      54      51      53      54      54      54
##   [54,]      53      54      54      51      53      54      54      54
##   [55,]      54      54      54      52      53      54      54      54
##   [56,]      54      54      54      52      53      54      54      54
##   [57,]      54      54      54      52      53      54      54      54
##   [58,]      54      54      54      52      54      54      54      54
##   [59,]      54      54      54      52      54      54      54      54
##   [60,]      54      54      54      52      54      54      54      54
##   [61,]      54      54      54      52      54      54      54      54
##   [62,]      54      54      54      52      54      54      54      54
##   [63,]      54      54      54      53      54      54      54      55
##   [64,]      54      54      54      53      54      55      55      55
##   [65,]      54      54      54      53      54      55      55      55
##   [66,]      54      55      55      53      54      55      55      55
##   [67,]      55      55      55      53      54      55      55      55
##   [68,]      55      55      55      53      55      55      55      55
##   [69,]      55      55      55      53      55      55      55      55
##   [70,]      55      55      55      53      55      55      55      55
##   [71,]      55      55      55      53      55      55      55      55
##   [72,]      55      55      55      53      55      55      55      55
##   [73,]      55      55      55      54      55      55      55      55
##   [74,]      55      55      55      54      55      55      55      55
##   [75,]      55      55      55      54      55      55      56      56
##   [76,]      55      55      55      54      55      56      56      56
##   [77,]      55      55      55      54      55      56      56      56
##   [78,]      55      55      55      54      56      56      56      56
##   [79,]      56      56      56      54      56      56      56      56
##   [80,]      56      56      56      55      56      56      56      56
##   [81,]      56      56      56      55      56      56      56      56
##   [82,]      56      56      56      55      56      56      56      56
##   [83,]      56      56      56      55      56      56      56      56
##         [,1137] [,1138] [,1139] [,1140] [,1141] [,1142] [,1143] [,1144]
##    [1,]      30      31      32      33      33      33      33      33
##    [2,]      39      40      41      42      42      42      42      42
##    [3,]      46      47      48      49      49      49      49      49
##    [4,]      49      50      52      53      54      54      54      54
##    [5,]      50      51      53      55      56      56      56      56
##    [6,]      50      51      53      55      56      56      56      56
##    [7,]      50      51      53      55      56      56      56      56
##    [8,]      50      51      53      55      56      56      56      56
##    [9,]      50      51      54      55      56      56      56      56
##   [10,]      50      51      54      55      56      56      56      56
##   [11,]      50      51      54      55      56      56      56      56
##   [12,]      51      51      54      55      56      56      56      56
##   [13,]      51      51      54      55      56      56      56      56
##   [14,]      51      51      54      55      56      56      56      56
##   [15,]      51      51      54      56      56      56      56      56
##   [16,]      51      51      54      56      56      56      56      56
##   [17,]      51      51      54      56      56      56      56      57
##   [18,]      51      51      54      56      56      56      57      57
##   [19,]      51      51      54      56      56      56      57      57
##   [20,]      51      51      54      56      56      56      57      57
##   [21,]      51      51      54      56      56      57      57      57
##   [22,]      51      51      54      56      56      57      57      57
##   [23,]      51      51      55      56      56      57      57      57
##   [24,]      52      52      55      56      56      57      57      57
##   [25,]      52      52      55      56      56      57      57      57
##   [26,]      52      52      55      56      56      57      57      57
##   [27,]      52      52      55      56      57      57      57      57
##   [28,]      52      52      55      56      57      57      57      57
##   [29,]      52      52      55      56      57      57      57      57
##   [30,]      52      52      55      56      57      57      57      57
##   [31,]      52      52      55      56      57      57      57      57
##   [32,]      52      52      55      56      57      57      57      57
##   [33,]      52      52      55      56      57      57      57      57
##   [34,]      52      52      55      56      57      57      57      57
##   [35,]      52      53      55      56      57      57      57      57
##   [36,]      53      53      56      57      57      57      57      57
##   [37,]      53      53      56      57      57      57      57      57
##   [38,]      53      53      56      57      57      57      57      57
##   [39,]      53      53      56      57      57      57      57      57
##   [40,]      53      53      56      57      57      57      57      57
##   [41,]      53      53      56      57      57      57      57      57
##   [42,]      53      53      56      57      57      57      57      57
##   [43,]      53      53      56      57      57      57      57      57
##   [44,]      53      53      56      57      57      57      57      57
##   [45,]      53      53      56      57      57      57      57      57
##   [46,]      53      53      56      57      57      57      57      57
##   [47,]      53      55      57      57      57      57      57      58
##   [48,]      53      55      57      57      57      57      57      58
##   [49,]      53      55      57      57      57      57      57      58
##   [50,]      53      55      57      57      57      57      57      58
##   [51,]      54      55      57      57      57      57      57      58
##   [52,]      54      55      57      57      57      57      57      58
##   [53,]      54      55      57      57      57      57      58      58
##   [54,]      54      55      57      57      57      57      58      58
##   [55,]      54      55      57      57      57      57      58      58
##   [56,]      54      55      57      57      57      57      58      58
##   [57,]      54      56      57      57      57      57      58      58
##   [58,]      54      56      57      57      57      58      58      58
##   [59,]      54      56      57      57      57      58      58      58
##   [60,]      54      56      57      57      57      58      58      58
##   [61,]      54      56      57      57      57      58      58      58
##   [62,]      54      56      57      57      57      58      58      58
##   [63,]      55      56      57      57      57      58      58      58
##   [64,]      55      56      57      57      57      58      58      58
##   [65,]      55      56      57      57      58      58      58      58
##   [66,]      55      56      57      57      58      58      58      58
##   [67,]      55      57      57      57      58      58      58      58
##   [68,]      55      57      57      57      58      58      58      58
##   [69,]      55      57      57      57      58      58      58      58
##   [70,]      55      57      57      57      58      58      58      59
##   [71,]      55      57      57      57      58      58      58      59
##   [72,]      55      57      57      57      58      58      58      59
##   [73,]      55      57      57      57      58      58      58      59
##   [74,]      55      57      57      57      58      58      58      59
##   [75,]      56      57      57      58      58      58      58      59
##   [76,]      56      57      57      58      58      58      59      59
##   [77,]      56      57      57      58      58      58      59      59
##   [78,]      56      57      57      58      58      58      59      59
##   [79,]      56      57      57      58      58      58      59      59
##   [80,]      56      57      57      58      58      58      59      59
##   [81,]      56      57      57      58      58      58      59      59
##   [82,]      56      57      57      58      58      58      59      59
##   [83,]      56      57      57      58      58      59      59      59
##         [,1145] [,1146] [,1147] [,1148] [,1149] [,1150] [,1151] [,1152]
##    [1,]      33      33      34      34      34      33      33      33
##    [2,]      42      42      43      42      42      41      41      41
##    [3,]      49      49      50      49      48      47      47      47
##    [4,]      54      54      54      52      51      50      50      50
##    [5,]      56      56      55      53      51      51      50      50
##    [6,]      56      56      56      53      51      51      51      51
##    [7,]      56      56      56      53      52      51      51      51
##    [8,]      56      56      56      53      52      51      51      51
##    [9,]      56      56      56      53      52      51      51      51
##   [10,]      56      56      56      53      52      51      51      51
##   [11,]      56      56      56      53      52      51      51      51
##   [12,]      56      56      56      53      52      52      52      52
##   [13,]      56      56      56      53      52      52      52      52
##   [14,]      56      56      57      53      52      52      52      52
##   [15,]      56      57      57      53      52      52      52      52
##   [16,]      57      57      57      53      52      52      52      52
##   [17,]      57      57      57      53      53      53      53      53
##   [18,]      57      57      57      54      53      53      53      53
##   [19,]      57      57      57      54      53      53      53      53
##   [20,]      57      57      57      54      53      53      53      53
##   [21,]      57      57      57      54      53      53      53      53
##   [22,]      57      57      57      54      53      53      53      53
##   [23,]      57      57      56      54      53      53      53      53
##   [24,]      57      57      56      54      54      54      54      54
##   [25,]      57      57      56      54      54      54      54      54
##   [26,]      57      57      56      54      54      54      54      54
##   [27,]      57      57      56      54      54      54      54      54
##   [28,]      57      57      56      55      54      54      54      54
##   [29,]      57      57      56      55      54      54      54      54
##   [30,]      57      57      56      55      55      55      55      55
##   [31,]      57      57      56      55      55      55      55      55
##   [32,]      57      57      56      55      55      55      55      55
##   [33,]      57      57      56      55      55      55      55      55
##   [34,]      57      57      56      55      55      55      55      55
##   [35,]      57      57      56      56      56      56      56      56
##   [36,]      57      57      56      56      56      56      56      56
##   [37,]      57      57      56      56      56      56      56      56
##   [38,]      57      57      56      56      56      56      56      56
##   [39,]      57      57      56      56      56      56      56      56
##   [40,]      57      57      57      56      56      56      56      56
##   [41,]      57      57      57      57      57      57      57      57
##   [42,]      57      57      57      57      57      57      57      57
##   [43,]      57      57      57      57      57      57      57      57
##   [44,]      58      57      57      57      57      57      57      57
##   [45,]      58      58      58      58      58      58      58      58
##   [46,]      58      58      58      58      58      58      58      58
##   [47,]      58      58      58      58      58      58      58      58
##   [48,]      58      58      58      58      58      58      58      58
##   [49,]      58      58      58      58      58      58      58      58
##   [50,]      58      58      58      58      58      58      58      58
##   [51,]      58      58      58      58      58      58      58      58
##   [52,]      58      58      58      58      58      58      58      58
##   [53,]      58      58      58      58      58      58      58      59
##   [54,]      58      58      58      58      58      58      59      59
##   [55,]      58      58      58      58      58      58      59      59
##   [56,]      58      58      58      58      58      59      59      59
##   [57,]      58      58      58      58      58      59      59      59
##   [58,]      58      58      58      58      59      59      59      59
##   [59,]      58      58      58      58      59      59      59      59
##   [60,]      58      58      58      59      59      59      59      59
##   [61,]      58      58      58      59      59      59      59      59
##   [62,]      58      58      58      59      59      59      59      59
##   [63,]      58      58      59      59      59      59      59      59
##   [64,]      58      58      59      59      59      59      59      59
##   [65,]      58      58      59      59      59      59      59      59
##   [66,]      58      59      59      59      59      59      59      59
##   [67,]      58      59      59      59      59      59      59      59
##   [68,]      59      59      59      59      59      59      59      59
##   [69,]      59      59      59      59      59      59      59      59
##   [70,]      59      59      59      59      59      59      59      59
##   [71,]      59      59      59      59      59      59      59      59
##   [72,]      59      59      59      59      59      59      59      59
##   [73,]      59      59      59      59      59      59      59      59
##   [74,]      59      59      59      59      59      59      59      59
##   [75,]      59      59      59      59      59      59      59      59
##   [76,]      59      59      59      59      59      59      59      60
##   [77,]      59      59      59      59      59      59      60      60
##   [78,]      59      59      59      59      59      59      60      60
##   [79,]      59      59      59      59      59      60      60      60
##   [80,]      59      59      59      59      59      60      60      60
##   [81,]      59      59      59      59      60      60      60      60
##   [82,]      59      59      59      59      60      60      60      60
##   [83,]      59      59      59      59      60      60      60      60
##         [,1153] [,1154] [,1155] [,1156] [,1157] [,1158] [,1159] [,1160]
##    [1,]      34      34      35      35      35      35      35      34
##    [2,]      41      41      42      42      42      42      42      41
##    [3,]      47      47      47      47      47      47      46      45
##    [4,]      50      50      50      50      50      49      48      46
##    [5,]      50      50      50      50      50      50      47      46
##    [6,]      50      50      50      50      50      50      47      46
##    [7,]      51      51      51      51      51      51      48      46
##    [8,]      51      51      51      51      51      51      48      46
##    [9,]      51      51      51      51      51      51      48      46
##   [10,]      51      51      51      51      51      51      48      47
##   [11,]      51      51      51      51      51      51      48      47
##   [12,]      52      52      52      52      52      52      49      47
##   [13,]      52      52      52      52      52      52      49      48
##   [14,]      52      52      52      52      52      52      49      48
##   [15,]      52      52      52      52      52      52      49      48
##   [16,]      52      52      52      52      52      52      49      48
##   [17,]      53      53      53      53      53      53      50      49
##   [18,]      53      53      53      53      53      53      50      49
##   [19,]      53      53      53      53      53      53      50      49
##   [20,]      53      53      53      53      53      53      50      49
##   [21,]      53      53      53      53      53      53      51      50
##   [22,]      53      53      53      53      53      53      51      50
##   [23,]      53      53      53      53      54      54      51      51
##   [24,]      54      54      54      54      54      54      51      51
##   [25,]      54      54      54      54      54      54      52      51
##   [26,]      54      54      54      54      54      54      52      51
##   [27,]      54      54      54      54      54      54      52      52
##   [28,]      54      54      54      54      55      55      52      52
##   [29,]      54      54      54      55      55      55      53      52
##   [30,]      55      55      55      55      55      55      53      53
##   [31,]      55      55      55      55      55      55      53      53
##   [32,]      55      55      55      55      55      55      54      53
##   [33,]      55      55      55      55      55      55      54      54
##   [34,]      55      55      55      56      56      56      54      54
##   [35,]      56      56      56      56      56      56      55      54
##   [36,]      56      56      56      56      56      56      55      55
##   [37,]      56      56      56      56      56      56      55      55
##   [38,]      56      56      56      56      56      56      55      55
##   [39,]      56      56      56      56      56      56      56      56
##   [40,]      56      56      56      57      57      57      56      56
##   [41,]      57      57      57      57      57      57      56      56
##   [42,]      57      57      57      57      57      57      57      56
##   [43,]      57      57      57      57      57      57      57      57
##   [44,]      57      57      57      57      57      57      57      57
##   [45,]      58      58      58      58      58      58      58      58
##   [46,]      58      58      58      58      58      58      58      58
##   [47,]      58      58      58      58      58      59      59      59
##   [48,]      58      58      58      58      59      59      59      59
##   [49,]      58      58      58      58      58      58      59      59
##   [50,]      58      58      58      58      58      58      58      58
##   [51,]      58      58      58      58      58      58      58      58
##   [52,]      58      58      58      58      58      58      58      58
##   [53,]      59      59      59      59      59      59      59      59
##   [54,]      59      59      59      59      59      59      59      59
##   [55,]      59      59      59      59      59      59      59      59
##   [56,]      59      59      59      59      59      59      59      59
##   [57,]      59      59      59      59      59      59      59      59
##   [58,]      59      59      59      59      59      59      59      59
##   [59,]      59      59      59      59      59      59      59      59
##   [60,]      59      59      59      59      59      59      59      59
##   [61,]      59      59      59      59      59      59      59      59
##   [62,]      59      59      59      59      59      59      59      59
##   [63,]      59      59      59      59      59      59      59      59
##   [64,]      59      59      59      59      59      59      59      60
##   [65,]      59      59      59      59      59      59      59      60
##   [66,]      59      59      59      59      59      59      60      60
##   [67,]      59      59      59      59      59      60      60      60
##   [68,]      59      59      59      59      60      60      60      60
##   [69,]      59      59      59      59      60      60      60      60
##   [70,]      59      59      59      60      60      60      60      60
##   [71,]      59      59      59      60      60      60      60      60
##   [72,]      59      59      60      60      60      60      60      60
##   [73,]      59      60      60      60      60      60      60      60
##   [74,]      59      60      60      60      60      60      60      60
##   [75,]      60      60      60      60      60      60      60      60
##   [76,]      60      60      60      60      60      60      60      60
##   [77,]      60      60      60      60      60      60      60      60
##   [78,]      60      60      60      60      60      60      60      60
##   [79,]      60      60      60      60      60      60      60      60
##   [80,]      60      60      60      60      60      60      60      60
##   [81,]      60      60      60      60      60      60      60      60
##   [82,]      60      60      60      60      60      60      60      60
##   [83,]      60      60      60      60      60      60      60      60
##         [,1161] [,1162] [,1163] [,1164] [,1165] [,1166] [,1167] [,1168]
##    [1,]      34      33      32      32      32      32      33      33
##    [2,]      39      38      37      36      35      35      35      37
##    [3,]      43      42      40      38      38      38      38      40
##    [4,]      45      43      41      39      39      38      39      41
##    [5,]      45      43      40      39      39      39      40      42
##    [6,]      45      43      40      39      39      39      40      42
##    [7,]      45      44      41      40      39      39      40      42
##    [8,]      46      44      41      40      40      40      41      43
##    [9,]      46      44      42      41      41      40      41      44
##   [10,]      46      44      42      41      41      41      42      45
##   [11,]      46      45      43      42      42      42      42      45
##   [12,]      47      45      43      42      42      42      42      46
##   [13,]      47      46      43      42      42      42      42      46
##   [14,]      47      45      44      43      43      43      43      47
##   [15,]      48      45      44      43      43      43      43      47
##   [16,]      48      45      44      44      44      44      44      47
##   [17,]      48      46      44      44      44      44      44      48
##   [18,]      49      46      45      45      45      45      45      48
##   [19,]      49      46      45      45      45      45      45      49
##   [20,]      49      47      46      46      46      46      47      49
##   [21,]      50      47      46      46      46      46      48      50
##   [22,]      50      48      47      47      47      47      48      50
##   [23,]      50      48      47      47      47      47      49      51
##   [24,]      51      48      48      48      48      48      49      51
##   [25,]      51      49      48      48      48      48      49      51
##   [26,]      51      49      49      49      49      49      50      52
##   [27,]      52      49      49      49      49      49      50      52
##   [28,]      52      50      50      49      49      50      51      53
##   [29,]      52      50      50      50      50      50      51      53
##   [30,]      53      51      51      51      51      51      53      53
##   [31,]      53      51      51      51      51      51      53      54
##   [32,]      53      52      51      51      51      52      54      54
##   [33,]      54      52      52      52      52      52      54      54
##   [34,]      54      53      52      52      52      53      55      55
##   [35,]      54      53      53      53      53      53      55      55
##   [36,]      55      54      53      53      53      54      55      56
##   [37,]      55      54      54      54      54      54      55      56
##   [38,]      55      54      54      54      54      55      56      56
##   [39,]      56      55      55      55      55      55      56      57
##   [40,]      56      55      55      55      55      56      57      57
##   [41,]      56      56      56      56      56      56      57      57
##   [42,]      56      56      56      56      56      57      57      58
##   [43,]      57      57      57      57      57      57      58      58
##   [44,]      57      57      57      57      57      58      58      59
##   [45,]      58      58      58      58      58      58      59      59
##   [46,]      59      59      59      59      59      59      59      59
##   [47,]      59      59      59      59      59      59      59      59
##   [48,]      59      59      59      59      59      59      59      59
##   [49,]      59      59      59      59      59      59      59      59
##   [50,]      58      58      59      59      59      59      59      59
##   [51,]      58      58      59      59      59      59      59      59
##   [52,]      58      58      58      59      59      59      59      59
##   [53,]      59      59      59      59      59      59      59      59
##   [54,]      59      59      59      59      59      59      59      59
##   [55,]      59      59      59      59      59      59      59      59
##   [56,]      59      59      59      59      59      59      59      59
##   [57,]      59      59      59      59      59      59      59      59
##   [58,]      59      59      59      59      59      59      59      59
##   [59,]      59      59      59      59      59      59      59      59
##   [60,]      59      59      59      59      59      59      59      60
##   [61,]      59      59      59      59      59      60      60      60
##   [62,]      59      59      60      60      60      60      60      60
##   [63,]      59      60      60      60      60      60      60      60
##   [64,]      60      60      60      60      60      60      60      60
##   [65,]      60      60      60      60      60      60      60      60
##   [66,]      60      60      60      60      60      60      60      60
##   [67,]      60      60      60      60      60      60      60      60
##   [68,]      60      60      60      60      60      60      60      60
##   [69,]      60      60      60      60      60      60      60      60
##   [70,]      60      60      60      60      60      60      60      60
##   [71,]      60      60      60      60      60      60      60      60
##   [72,]      60      60      60      60      60      60      60      60
##   [73,]      60      60      60      60      60      60      60      60
##   [74,]      60      60      60      60      60      60      60      60
##   [75,]      60      60      60      60      60      60      60      60
##   [76,]      60      60      60      60      60      60      60      60
##   [77,]      60      60      60      60      60      60      60      60
##   [78,]      60      60      60      60      60      60      60      60
##   [79,]      60      60      60      60      60      60      60      60
##   [80,]      60      60      60      60      60      60      60      60
##   [81,]      60      60      60      60      60      60      60      60
##   [82,]      60      60      60      60      60      60      60      60
##   [83,]      60      60      60      60      60      60      60      60
##         [,1169] [,1170] [,1171] [,1172] [,1173] [,1174] [,1175] [,1176]
##    [1,]      34      35      35      34      34      34      34      34
##    [2,]      38      39      39      38      37      36      36      36
##    [3,]      41      42      41      40      38      38      38      38
##    [4,]      43      43      41      40      39      38      38      38
##    [5,]      44      44      41      40      39      39      39      39
##    [6,]      44      44      42      40      40      39      39      39
##    [7,]      44      44      42      41      40      40      40      39
##    [8,]      45      45      43      41      40      40      40      40
##    [9,]      45      45      43      42      41      41      41      40
##   [10,]      46      46      43      42      42      41      41      41
##   [11,]      46      46      44      42      42      42      42      41
##   [12,]      47      47      44      43      43      43      42      42
##   [13,]      47      47      45      43      43      43      43      42
##   [14,]      48      48      45      44      44      43      43      42
##   [15,]      48      48      45      44      44      44      43      43
##   [16,]      48      49      46      45      45      44      44      43
##   [17,]      49      49      46      45      45      45      44      44
##   [18,]      49      49      47      46      46      46      45      44
##   [19,]      49      50      47      46      46      46      45      45
##   [20,]      50      50      48      47      47      46      46      45
##   [21,]      50      51      48      48      47      47      46      46
##   [22,]      51      51      49      48      48      48      47      46
##   [23,]      51      51      49      48      48      48      47      47
##   [24,]      51      52      49      49      49      49      48      47
##   [25,]      52      52      50      49      49      49      48      47
##   [26,]      52      52      50      50      50      49      49      48
##   [27,]      53      53      51      50      51      50      49      49
##   [28,]      53      53      51      51      51      51      50      49
##   [29,]      53      53      52      52      52      51      50      50
##   [30,]      54      54      52      52      52      52      51      51
##   [31,]      54      54      53      53      53      52      52      51
##   [32,]      54      55      53      53      53      53      52      51
##   [33,]      55      55      54      54      54      53      53      52
##   [34,]      55      55      54      55      55      54      53      53
##   [35,]      56      56      55      55      55      54      54      53
##   [36,]      56      56      55      55      56      55      54      53
##   [37,]      56      56      56      56      56      55      55      54
##   [38,]      56      57      56      56      56      56      55      54
##   [39,]      57      57      57      57      57      56      56      55
##   [40,]      57      57      57      58      58      57      56      56
##   [41,]      58      58      58      58      58      58      57      56
##   [42,]      58      58      58      59      59      58      58      57
##   [43,]      58      59      59      59      59      59      58      58
##   [44,]      59      59      59      60      60      60      59      58
##   [45,]      59      60      60      60      60      60      60      59
##   [46,]      60      60      60      60      60      60      60      60
##   [47,]      60      60      60      60      60      60      60      60
##   [48,]      59      60      60      60      60      60      60      60
##   [49,]      59      59      60      60      60      60      60      60
##   [50,]      59      59      59      60      60      60      60      60
##   [51,]      59      59      59      60      60      60      60      60
##   [52,]      59      59      59      59      60      60      60      60
##   [53,]      59      59      59      59      60      60      60      60
##   [54,]      59      59      59      59      60      60      60      60
##   [55,]      59      59      59      60      60      60      60      60
##   [56,]      59      59      59      59      60      60      60      60
##   [57,]      59      59      59      59      59      59      59      60
##   [58,]      59      59      59      59      59      59      59      59
##   [59,]      59      59      59      59      59      59      59      59
##   [60,]      60      60      60      60      60      60      60      60
##   [61,]      60      60      60      60      60      60      60      60
##   [62,]      60      60      60      60      60      60      60      60
##   [63,]      60      60      60      60      60      60      60      60
##   [64,]      60      60      60      60      60      60      60      60
##   [65,]      60      60      60      60      60      60      60      60
##   [66,]      60      60      60      60      60      60      60      60
##   [67,]      60      60      60      60      60      60      60      60
##   [68,]      60      60      60      60      60      60      60      60
##   [69,]      60      60      60      60      60      60      60      60
##   [70,]      60      60      60      60      60      60      60      60
##   [71,]      60      60      60      60      60      60      60      60
##   [72,]      60      60      60      60      60      60      60      60
##   [73,]      60      60      60      60      60      60      60      60
##   [74,]      60      60      60      60      60      60      60      60
##   [75,]      60      60      60      60      60      60      60      60
##   [76,]      60      60      60      60      60      60      60      60
##   [77,]      60      60      60      60      60      60      60      60
##   [78,]      60      60      60      60      60      60      60      60
##   [79,]      60      60      60      60      60      60      60      60
##   [80,]      60      60      60      60      60      60      60      60
##   [81,]      60      60      60      60      60      60      60      60
##   [82,]      60      60      60      60      60      60      60      60
##   [83,]      60      60      60      60      60      60      60      60
##         [,1177] [,1178] [,1179] [,1180] [,1181] [,1182] [,1183] [,1184]
##    [1,]      35      36      38      39      40      40      39      38
##    [2,]      37      38      38      38      38      38      37      36
##    [3,]      38      38      38      37      37      37      35      34
##    [4,]      38      38      38      38      38      37      35      33
##    [5,]      39      38      38      38      38      38      35      33
##    [6,]      39      39      38      38      38      38      35      33
##    [7,]      39      39      39      39      38      38      35      34
##    [8,]      40      39      39      39      38      38      35      34
##    [9,]      40      40      39      39      39      38      35      34
##   [10,]      40      40      40      39      39      38      35      34
##   [11,]      41      40      40      39      39      38      36      35
##   [12,]      41      41      40      40      39      38      36      35
##   [13,]      42      41      40      40      39      38      36      35
##   [14,]      42      41      41      40      39      38      36      35
##   [15,]      42      42      41      40      39      38      37      36
##   [16,]      43      42      41      40      39      38      37      36
##   [17,]      43      42      41      41      39      38      37      37
##   [18,]      43      42      42      41      40      39      38      37
##   [19,]      44      43      42      41      40      39      38      37
##   [20,]      44      44      43      42      41      40      39      38
##   [21,]      45      44      44      43      42      41      40      39
##   [22,]      46      45      44      43      42      42      41      40
##   [23,]      46      45      45      44      43      42      42      41
##   [24,]      46      46      45      44      43      43      42      41
##   [25,]      47      46      46      45      44      43      42      42
##   [26,]      48      47      46      46      45      44      43      43
##   [27,]      48      48      47      46      45      45      44      44
##   [28,]      49      48      48      47      46      45      45      44
##   [29,]      49      49      48      47      46      46      45      45
##   [30,]      50      49      49      48      47      46      46      45
##   [31,]      50      50      49      48      47      47      46      46
##   [32,]      51      50      49      48      48      47      47      46
##   [33,]      51      51      50      49      48      48      47      46
##   [34,]      52      51      50      49      49      48      47      47
##   [35,]      52      51      51      50      49      48      48      47
##   [36,]      53      52      51      50      49      49      48      48
##   [37,]      53      52      51      51      50      49      49      48
##   [38,]      53      53      52      51      50      50      49      49
##   [39,]      54      54      53      52      51      51      50      49
##   [40,]      55      55      54      53      52      52      51      50
##   [41,]      56      55      54      53      53      52      52      51
##   [42,]      56      56      55      54      53      53      52      52
##   [43,]      57      56      55      54      54      53      53      52
##   [44,]      58      56      56      55      54      53      53      52
##   [45,]      58      57      56      55      55      54      53      52
##   [46,]      60      58      57      56      56      55      54      53
##   [47,]      60      60      59      58      58      57      56      55
##   [48,]      60      60      60      60      60      59      58      57
##   [49,]      60      60      60      60      60      60      60      59
##   [50,]      60      60      62      62      60      60      60      60
##   [51,]      60      61      64      67      64      60      60      60
##   [52,]      60      63      69      76      71      65      62      60
##   [53,]      60      65      74      88      77      70      65      61
##   [54,]      60      64      74      84      81      73      67      62
##   [55,]      60      60      60      65      72      71      67      62
##   [56,]      60      60      60      60      62      63      64      62
##   [57,]      60      60      60      60      60      61      61      61
##   [58,]      60      60      60      60      60      60      60      60
##   [59,]      60      60      60      60      60      60      60      60
##   [60,]      60      60      60      60      60      60      60      60
##   [61,]      60      60      60      60      60      60      60      60
##   [62,]      60      60      60      60      60      60      60      60
##   [63,]      60      60      60      60      60      60      60      60
##   [64,]      60      60      60      60      60      60      60      60
##   [65,]      60      60      60      60      60      60      60      60
##   [66,]      60      60      60      60      60      60      60      60
##   [67,]      60      60      60      60      60      60      60      60
##   [68,]      60      60      60      60      60      60      60      60
##   [69,]      60      60      60      60      60      60      60      60
##   [70,]      60      60      60      60      60      60      60      60
##   [71,]      60      60      60      60      60      60      60      60
##   [72,]      60      60      60      60      60      60      60      60
##   [73,]      60      60      60      60      60      60      60      60
##   [74,]      60      60      60      60      60      60      60      60
##   [75,]      60      60      60      60      60      60      60      60
##   [76,]      60      60      60      60      60      60      60      60
##   [77,]      60      60      60      60      60      60      60      60
##   [78,]      60      60      60      60      60      60      60      60
##   [79,]      60      60      60      60      60      60      60      60
##   [80,]      60      60      60      60      60      60      60      60
##   [81,]      60      60      60      60      60      60      60      60
##   [82,]      60      60      60      60      60      60      60      60
##   [83,]      60      60      60      60      60      60      60      60
##         [,1185] [,1186] [,1187] [,1188] [,1189] [,1190] [,1191] [,1192]
##    [1,]      38      37      36      35      35      34      33      32
##    [2,]      35      34      34      33      33      32      32      31
##    [3,]      33      32      32      31      32      31      31      30
##    [4,]      32      32      32      31      31      31      30      29
##    [5,]      32      32      32      32      32      31      30      30
##    [6,]      33      32      32      32      31      31      30      29
##    [7,]      33      32      32      32      31      30      30      29
##    [8,]      33      33      32      31      31      30      30      29
##    [9,]      33      33      32      31      31      30      29      29
##   [10,]      34      33      32      32      31      30      29      29
##   [11,]      34      33      32      32      31      30      29      29
##   [12,]      34      33      32      32      31      30      29      29
##   [13,]      34      33      33      32      31      30      30      29
##   [14,]      35      34      33      32      31      30      30      29
##   [15,]      35      34      33      32      31      30      30      29
##   [16,]      35      35      34      33      32      31      30      30
##   [17,]      36      35      34      33      32      31      31      30
##   [18,]      36      35      34      33      32      32      31      31
##   [19,]      37      36      35      34      33      32      32      31
##   [20,]      38      37      36      35      34      33      33      32
##   [21,]      39      38      37      35      35      34      34      33
##   [22,]      39      39      37      36      36      35      35      34
##   [23,]      40      39      38      37      37      36      35      35
##   [24,]      41      40      39      38      38      37      36      36
##   [25,]      41      41      40      39      39      38      37      37
##   [26,]      42      42      41      40      39      39      38      38
##   [27,]      43      42      42      41      40      39      39      39
##   [28,]      44      43      42      41      40      40      40      39
##   [29,]      44      43      42      42      41      40      40      39
##   [30,]      44      44      43      42      41      41      40      40
##   [31,]      45      44      43      42      42      41      41      40
##   [32,]      45      44      43      43      42      42      41      40
##   [33,]      46      45      44      43      43      42      41      41
##   [34,]      46      45      44      44      43      42      42      41
##   [35,]      47      46      45      44      44      43      42      41
##   [36,]      47      46      45      45      44      43      43      42
##   [37,]      47      46      46      45      44      44      43      42
##   [38,]      48      47      46      46      45      44      44      43
##   [39,]      49      48      47      46      46      45      45      44
##   [40,]      49      49      48      47      47      46      46      45
##   [41,]      50      49      48      48      47      47      46      45
##   [42,]      51      49      49      48      48      47      46      46
##   [43,]      51      50      49      49      48      47      46      46
##   [44,]      51      50      49      49      48      47      46      45
##   [45,]      51      50      49      49      48      48      47      46
##   [46,]      52      51      51      50      49      49      48      47
##   [47,]      54      53      52      52      51      51      50      49
##   [48,]      56      55      55      55      55      54      54      53
##   [49,]      59      58      58      59      59      59      58      57
##   [50,]      60      61      60      60      60      59      59      58
##   [51,]      60      60      60      60      60      60      60      59
##   [52,]      60      60      60      60      60      60      60      60
##   [53,]      60      60      60      60      60      60      60      60
##   [54,]      60      60      60      60      60      60      60      60
##   [55,]      60      60      60      60      60      60      60      60
##   [56,]      60      60      60      60      60      60      60      60
##   [57,]      60      60      60      60      60      60      61      61
##   [58,]      60      59      60      60      60      61      61      62
##   [59,]      60      60      60      60      60      60      60      61
##   [60,]      60      58      59      60      62      64      66      68
##   [61,]      60      57      59      60      63      67      70      73
##   [62,]      60      56      58      60      65      70      74      79
##   [63,]      60      55      58      61      67      72      78      83
##   [64,]      60      54      58      61      68      75      82      88
##   [65,]      60      53      57      61      69      77      84      91
##   [66,]      60      54      57      61      70      77      85      92
##   [67,]      60      54      58      61      70      77      85      92
##   [68,]      60      54      57      61      69      77      84      91
##   [69,]      60      54      57      60      66      72      78      84
##   [70,]      60      55      57      60      63      67      72      76
##   [71,]      60      57      58      60      62      64      67      69
##   [72,]      60      59      59      60      61      62      63      64
##   [73,]      60      60      60      60      60      60      61      61
##   [74,]      60      60      60      60      60      60      60      60
##   [75,]      60      60      60      60      60      60      60      60
##   [76,]      60      60      60      60      60      60      60      60
##   [77,]      60      60      60      60      60      60      60      60
##   [78,]      60      60      60      60      60      60      60      60
##   [79,]      60      60      60      60      60      60      60      60
##   [80,]      60      60      60      60      60      60      60      60
##   [81,]      60      60      60      60      60      60      60      60
##   [82,]      60      60      60      60      60      60      60      60
##   [83,]      60      60      60      60      60      60      60      60
##         [,1193] [,1194] [,1195] [,1196] [,1197] [,1198] [,1199] [,1200]
##    [1,]      31      30      29      29      29      30      30      30
##    [2,]      29      29      28      29      29      29      30      30
##    [3,]      27      26      26      27      28      28      29      30
##    [4,]      26      26      26      27      28      29      30      31
##    [5,]      26      26      26      28      29      30      31      33
##    [6,]      26      26      26      28      30      31      33      37
##    [7,]      28      27      26      26      27      29      32      39
##    [8,]      28      27      27      27      28      30      33      40
##    [9,]      28      27      27      26      28      30      33      42
##   [10,]      28      27      27      26      28      30      33      42
##   [11,]      29      27      26      26      27      29      32      41
##   [12,]      28      28      27      26      26      27      29      38
##   [13,]      28      28      27      26      26      26      28      32
##   [14,]      28      28      27      26      26      26      28      31
##   [15,]      30      28      26      25      25      26      28      34
##   [16,]      30      28      26      25      25      26      28      34
##   [17,]      30      28      26      25      25      26      28      33
##   [18,]      28      28      28      29      29      30      31      33
##   [19,]      31      29      28      26      26      27      29      31
##   [20,]      32      30      29      27      27      28      30      32
##   [21,]      33      32      30      29      29      30      32      33
##   [22,]      33      33      32      32      31      31      32      36
##   [23,]      34      33      33      32      32      32      33      35
##   [24,]      35      34      34      33      32      32      33      35
##   [25,]      36      35      35      34      34      34      35      36
##   [26,]      37      37      37      36      36      36      37      38
##   [27,]      38      38      37      37      37      37      38      39
##   [28,]      39      38      38      37      37      37      38      39
##   [29,]      39      38      38      37      37      37      38      39
##   [30,]      39      39      38      38      37      37      38      39
##   [31,]      39      39      38      38      37      37      38      39
##   [32,]      39      39      39      38      38      38      39      40
##   [33,]      40      39      39      38      38      38      38      40
##   [34,]      40      39      39      38      38      38      39      40
##   [35,]      40      40      39      39      38      38      38      40
##   [36,]      41      40      40      39      39      38      38      41
##   [37,]      41      41      40      39      39      39      39      41
##   [38,]      42      41      41      40      40      40      40      42
##   [39,]      43      42      42      41      41      41      42      43
##   [40,]      44      44      43      43      43      43      44      45
##   [41,]      45      44      44      43      43      43      44      46
##   [42,]      45      44      44      43      43      44      44      46
##   [43,]      45      45      44      44      43      43      43      45
##   [44,]      45      44      43      42      41      42      43      44
##   [45,]      46      44      43      41      41      41      42      44
##   [46,]      44      44      44      44      44      45      45      45
##   [47,]      46      46      46      46      46      46      47      46
##   [48,]      50      49      49      49      49      49      49      48
##   [49,]      53      52      52      51      51      51      51      50
##   [50,]      58      56      56      55      54      54      53      53
##   [51,]      61      59      58      55      54      54      54      54
##   [52,]      59      59      59      58      58      58      58      58
##   [53,]      60      60      59      58      58      57      58      59
##   [54,]      60      60      60      59      59      59      59      60
##   [55,]      59      60      60      61      61      62      62      63
##   [56,]      60      60      60      62      62      63      64      66
##   [57,]      60      61      63      64      66      67      68      70
##   [58,]      62      65      66      68      69      71      72      74
##   [59,]      64      68      71      72      74      75      77      79
##   [60,]      73      75      78      80      81      82      83      83
##   [61,]      81      84      86      88      88      89      90      90
##   [62,]      90      93      96      97      97      98      98      98
##   [63,]      96      99     103     104     104     105     105     105
##   [64,]     102     107     110     110     110     111     111     111
##   [65,]     107     112     114     114     114     114     115     114
##   [66,]     103     111     116     119     122     122     122     119
##   [67,]     106     111     115     115     116     118     119     121
##   [68,]     105     111     115     115     117     118     120     121
##   [69,]      96     103     107     109     111     114     117     118
##   [70,]      84      89      94      98     102     106     110     113
##   [71,]      72      78      82      88      93      98     102     107
##   [72,]      62      68      71      78      84      90      96     100
##   [73,]      58      61      65      72      78      84      90      94
##   [74,]      56      59      62      69      74      80      86      91
##   [75,]      56      59      62      68      73      78      83      87
##   [76,]      56      59      62      67      71      76      81      84
##   [77,]      57      59      61      66      70      74      79      81
##   [78,]      57      59      61      66      70      73      77      79
##   [79,]      56      58      60      65      69      73      77      78
##   [80,]      56      58      60      64      68      72      77      78
##   [81,]      55      57      60      64      68      73      77      78
##   [82,]      55      57      60      64      68      73      78      79
##   [83,]      55      57      60      64      69      73      78      79
##         [,1201]
##    [1,]      31
##    [2,]      31
##    [3,]      31
##    [4,]      32
##    [5,]      34
##    [6,]      37
##    [7,]      41
##    [8,]      43
##    [9,]      45
##   [10,]      45
##   [11,]      44
##   [12,]      41
##   [13,]      37
##   [14,]      36
##   [15,]      37
##   [16,]      37
##   [17,]      36
##   [18,]      35
##   [19,]      35
##   [20,]      36
##   [21,]      37
##   [22,]      38
##   [23,]      38
##   [24,]      38
##   [25,]      39
##   [26,]      40
##   [27,]      41
##   [28,]      41
##   [29,]      41
##   [30,]      41
##   [31,]      41
##   [32,]      42
##   [33,]      42
##   [34,]      43
##   [35,]      43
##   [36,]      43
##   [37,]      43
##   [38,]      44
##   [39,]      45
##   [40,]      47
##   [41,]      48
##   [42,]      48
##   [43,]      48
##   [44,]      48
##   [45,]      47
##   [46,]      47
##   [47,]      48
##   [48,]      50
##   [49,]      52
##   [50,]      54
##   [51,]      56
##   [52,]      59
##   [53,]      61
##   [54,]      62
##   [55,]      64
##   [56,]      67
##   [57,]      70
##   [58,]      75
##   [59,]      79
##   [60,]      83
##   [61,]      89
##   [62,]      96
##   [63,]     103
##   [64,]     109
##   [65,]     112
##   [66,]     115
##   [67,]     120
##   [68,]     122
##   [69,]     120
##   [70,]     117
##   [71,]     113
##   [72,]     107
##   [73,]     102
##   [74,]      99
##   [75,]      96
##   [76,]      92
##   [77,]      89
##   [78,]      87
##   [79,]      87
##   [80,]      87
##   [81,]      88
##   [82,]      89
##   [83,]      89
##  [ reached getOption("max.print") -- omitted 1118 rows ]

Notice that we were able to use ncol on our RasterLayer object, because in some basic senses it behaves like a matrix, much as a Spatial*DataFrame behaves in some senses like a data.frame.

Explore the Structure

Can we create a new RasterLayer object from a matrix?

test = raster(matrix(DEM[,], ncol = ncol(DEM), byrow = TRUE))
test
## class      : RasterLayer 
## dimensions : 1201, 1201, 1442401  (nrow, ncol, ncell)
## resolution : 0.0008326395, 0.0008326395  (x, y)
## extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
## crs        : NA 
## source     : memory
## names      : layer 
## values     : 0, 976  (min, max)

We do get a new RasterLayer! However, notice that it of course has no projection, and has incorrect extent and resolution.

Explore the Structure

You can imagine that you could then use the DEM object’s information to assign the new RasterLayer its appropriate metadata (much like what we did with unprojected point data that we read in from a CSV and coerced to an sf object).

Because there’s a much easier way to do all of this…

Explore the Structure

Our subsetting operation can actually take a drop = FALSE argument!

DEM[10:15, 20:30, drop = FALSE]
## class      : RasterLayer 
## dimensions : 6, 11, 66  (nrow, ncol, ncell)
## resolution : 0.0008333333, 0.0008333333  (x, y)
## extent     : -122.9846, -122.9754, 37.98792, 37.99292  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=NAD27 +no_defs +ellps=clrk66 +nadgrids=@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat 
## source     : memory
## names      : layer 
## values     : 0, 41  (min, max)

And this gives us back a new RasterLayer object!

In essence, this makes the subsetting operation more or less like a basic clipping function.

Explore the Structure

Here’s what that gave us:

test = DEM[10:15, 20:30, drop = FALSE]
plot(test)

Explore the Structure

And now what does the @data@values slot look like in our new object now?

test@data@values
##  [1] 39 41 39 41 38 36 27 21 15  9  4 24 25 23 26 23 23 17 12  8  5  2 10
## [24] 11  9 11  9 10  7  4  2  1  0  2  2  2  2  2  2  2  1  0  0  0  0  0
## [47]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

Explore the Structure

That makes sense, because our test object didn’t come from a file, so R didn’t leave its data on disk.

test@data@inmemory
## [1] TRUE
test@data@fromdisk
## [1] FALSE

CRS Transformations

Check the CRS (aka projection) of the DEM raster data.

Transform (or reproject) the Tracts vector data to match it.

#check out its projection
proj4string(DEM)
## [1] "+proj=longlat +datum=NAD27 +no_defs +ellps=clrk66 +nadgrids=@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat"
#reproject tracts to our DEM projection
SFtracts_NAD = st_transform(SFtracts, st_crs(DEM))

CRS Transformations

You can reproject the DEM with raster::projectRaster

Note how the syntax is similar to sp::spTransform

DEM_WGS = projectRaster(DEM, projectExtent(DEM, st_crs(SFtracts)))
## Error in rgdal::rawTransform(projfrom, projto, nrow(xy), xy[, 1], xy[, : projection not named

CRS Transformations

Oops! What went wrong?

That’s not a very informative error message…

Let’s read the docs!

?projectRaster

CRS Transformations

Looks like projectRaster expects the crs argument needs to be an object of the (uppercase) ‘CRS’ class.

Is it?

class(st_crs(SFtracts))
## [1] "crs"

CRS Transformations

We need to be careful when working between the raster and sf packages, because raster is older and still depends on sp.

This object is of the (lowercase) crs class, which is a class defined by the sf package!

However, we can actually just extract the proj4string from our crs-class object and use that as our argument instead!

st_crs(SFtracts)$proj4string
## [1] "+proj=longlat +datum=NAD83 +no_defs"

CRS Transformations

So let’s try that again, giving the proj4string as our argument:

DEM_WGS = projectRaster(DEM, projectExtent(DEM, st_crs(SFtracts)$proj4string))

CRS Transformations

Then we can check equivalence.

st_crs(SFtracts_NAD) == st_crs(DEM)
## [1] TRUE
st_crs(DEM_WGS) == st_crs(SFtracts)
## [1] FALSE

CRS Transformations

What happened now?

It appears that sp and sf are using the same EPSG codes but building slightly different proj4string representations, perhaps because of differences in the projection databases used by the two.

st_crs(DEM_WGS)
## Coordinate Reference System:
##   EPSG: 4269 
##   proj4string: "+proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs"
st_crs(SFtracts)
## Coordinate Reference System:
##   EPSG: 4269 
##   proj4string: "+proj=longlat +datum=NAD83 +no_defs"

CRS Transformations

That should be alright though, as long as we know that our EPSG codes are identical, because each code identifies a materially distinct CRS.

st_crs(DEM_WGS)$epsg == st_crs(SFtracts)$epsg
## [1] TRUE

About the sp package

As we mentiond in Part I, sp was for a long time the primary geospatial package in R.

sf has now eclipsed this package (along with the ‘rgdal’ and ‘rgeos’ packages).

However, as you can see, not all geospatial packages have made the transition already.

sp package

You may sometimes run into issues such as the one we just experienced, where you can find an easy workaround.

Other times, however, you may actually need to work with sp objects instead of sf ones.

Luckily, this is easy!

sp package

To convert from sf to sp, sf provides the as_Spatial function.

Let’s convert SFhomes15_sf, then look at its string representation.

Note that it looks very similar to the metadata of a raster object.

SFhomes15_sp = as_Spatial(SFhomes15_sf)
SFhomes15_sp
## class       : SpatialPointsDataFrame 
## features    : 5849 
## extent      : -122.5107, -122.3696, 37.70821, 37.80612  (xmin, xmax, ymin, ymax)
## crs         : +proj=longlat +datum=NAD83 +no_defs +ellps=GRS80 +towgs84=0,0,0 
## variables   : 17
## names       : FiscalYear,  SalesDate,                              Address, YearBuilt, NumBedrooms, NumBathrooms, NumRooms, NumStories, NumUnits, AreaSquareFeet, ImprovementValue, LandValue,     Neighborhood,                              Location, SupeDistrict, ... 
## min values  :       2015, 2015-01-02, 0000 0000                       0000,        24,           0,            0,        0,          0,        0,              0,                0,         0,                 , (37.7082125474599, -122.456157054616),            1, ... 
## max values  :       2015, 2015-12-31, S000 3016 SACRAMENTO          ST0000,      2016,          13,           13,       43,         75,        9,          40000,          1979737,   2614268, Western Addition, (37.8061200328565, -122.419485868976),           11, ...

sp package

And look at its structure, which is also similar.

str(SFhomes15_sp)

sp package

That makes sense, because the raster and sp packages are designed to feel as standardized and consistent as possible.

There are differences, however!

Some are just stylistic:

  • @bbox instead of @extent
  • @proj4string instead of @crs

Some come from the difference between the vector and raster data models:

  • no dimensions attribute
  • no resolution (this is a concept for vector data, but is not key metadata)
  • the @data slot is a data.frame (a.k.a. an “attribute table”)

sp package

sp creates objects that pertain to any of a number of classes, which conform to the Spatial*DataFrame convention:

  • SpatialPointsDataFrame
  • SpatialLinesDataFrame
  • SpatialPolygonsDataFrame
  • etc.

sp package

Spatial objects can then be transformed, subsetted, analyzed, and plotted, using a variety of packages that may not be compatible (yet?) with sf.

Here’s a plot:

plot(SFhomes15_sp)

sp package

And if you need to convert from sp to sf, there’s a function for that too (which we already saw in Part 1!).

SFhomes15_sfagain = st_as_sf(SFhomes15_sp)
plot(SFhomes15_sfagain['totvalue'])

sp package

We will not go into any further detail on sp in this workshop.

However, if you find you need to learn more then please visit our former R geospatial workshop, which is based on sp.

(It uses the same data and runs more or less the same operations as this workshop, so it should be easy to follow and should highlight all the differences between sf and sp.)

Clipping Rasters

Since the raster data covers a larger area than our vector data / area of interest, we can clip it using the raster::crop function.

# clip the WGS CRS version of the rasters to SFtracts 
DEM_WGS_crop = crop(DEM_WGS, SFtracts)

# Clip the NAD CRS version
DEM_crop = crop(DEM, SFtracts_NAD)

Plot Clipped Raster data

You can plot raster and vector

plot(DEM_WGS_crop)

Plot Raster & Vector Data

And we can plot raster and vector data together!

Here we plot the NAD CRS version.

#plot together
plot(DEM_WGS_crop)
plot(st_geometry(SFtracts), add = T, col = NA)

Masking Raster Data

Notice that the clipping (or cropping) operation reduced our dataset to just the extent of the census-tract dataset.

But it still left us with values outside of the census tracts themselves (because they are areas outside the city of San Francisco).

Masking Raster Data

For some purposes, we may want to get rid of those values as well.

We can do this with an operation called masking.

DEM_WGS_crop_masked = mask(DEM_WGS_crop, SFtracts)

Masking Raster Data

Here’s what that gives us, compared to the unmasked object:

DEM_WGS_crop_masked
## class      : RasterLayer 
## dimensions : 187, 224, 41888  (nrow, ncol, ncell)
## resolution : 0.0008333674, 0.0008333165  (x, y)
## extent     : -122.5148, -122.3282, 37.70785, 37.86368  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=NAD83 +no_defs +ellps=GRS80 +towgs84=0,0,0 
## source     : memory
## names      : san_francisco.e 
## values     : 0, 269.8155  (min, max)
DEM_WGS_crop
## class      : RasterLayer 
## dimensions : 187, 224, 41888  (nrow, ncol, ncell)
## resolution : 0.0008333674, 0.0008333165  (x, y)
## extent     : -122.5148, -122.3282, 37.70785, 37.86368  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=NAD83 +no_defs +ellps=GRS80 +towgs84=0,0,0 
## source     : memory
## names      : san_francisco.e 
## values     : 0, 303.9775  (min, max)

Masking Raster Data

Still a rectangular grid of cells (because a raster will always be rectangular).

Still has the same nrow and ncol as the unmasked object.

What masking did was to set the cells that lie outside our dataset to NAs.

Masking Raster Data

plot(DEM_WGS_crop_masked)
plot(st_geometry(SFtracts), add = T, col = NA)

Plotting rasters in tmap

We can make an interactive plot using tmap

my_map <- tm_shape(DEM_WGS_crop_masked) +
  tm_raster() +
tm_shape(SFtracts) + 
  tm_borders() +

# Set mode to interactive
tmap_mode("view")

View Map

my_map

Writing Raster Data

And now that we’ve manipulated our data as desired, we can write it to disk if we like!

#write our reprojected, cropped data to the data directory, using the Geotiff format
#(and allow R to overwrite if file already exists)
writeRaster(DEM_WGS_crop_masked, filename="./data/DEM_reproject_crop.tif", format="GTiff", overwrite = T)

Section 2: Raster Operations and Spatial Analysis

Challenge section

This section will feature a number of challenges, to get you practicing some of the material we’ve already covered today.

Extract elevation values

We can use the raster::extract function to get the elevation values for each tract.

# get the elevation for every cell in each of the census tracts
elev = extract(DEM_WGS_crop, SFtracts)

#what did that give us?
head(elev)
## [[1]]
##  [1] 55.97961 57.98517 57.98980 58.99490 58.99491 58.99491 59.99493
##  [8] 59.99492 59.99492 59.99491 59.99998 60.00000 60.00000 60.00000
## [15] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [22] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## 
## [[2]]
##  [1] 59.00984 59.00487 59.00488 59.00002 59.00002 59.00000 58.00979
##  [8] 58.00487 58.00984 58.00485 58.00002 57.00977
## 
## [[3]]
##  [1] 57.98527 57.99014 57.99016 57.99015 59.00039 58.99510 58.99509
##  [8] 58.99508 59.99514 59.99511 59.99510 59.99510 60.00000 60.00000
## [15] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [22] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [29] 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000 60.00000
## [36] 60.00000
## 
## [[4]]
##  [1] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [24] 60 60 60 60 60 60 60 60 60 60 60
## 
## [[5]]
##  [1] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [24] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [47] 60
## 
## [[6]]
##  [1] 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60
## [24] 60 60 60 60 60 60 60 60 60 60 60 60 60

What is the output?

Check out the data in the elev object

length(elev)
## [1] 195
nrow(SFtracts)
## [1] 195

It’s a vector of the elevations for all the cells within each census tract!

Average Raster value by Vector shape

Let’s get each tract’s average elevation

mean_elev = lapply(elev, mean, na.rm = T)
head(mean_elev)
## [[1]]
## [1] 59.60425
## 
## [[2]]
## [1] 58.42156
## 
## [[3]]
## [1] 59.6645
## 
## [[4]]
## [1] 60
## 
## [[5]]
## [1] 60
## 
## [[6]]
## [1] 60

Add elevation to Vector object

Let’s add this to the SFtracts_NAD data.frame.

Note: the order remains the same, so we can just add this right in!

SFtracts$mean_elev = unlist(mean_elev)

Map it

#what did we get?
elev_map <- tm_shape(SFtracts) + 
  tm_polygons(col = 'mean_elev') +
  tm_layout("The pain of biking in SF, by census tract", 
            inner.margins=c(0,0,.1,0), title.size=4.8)

Map it

elev_map

One step Re-do

We can also pass a function argument to raster::extract

elev = extract(DEM_WGS_crop, SFtracts, fun=mean)

#what did that give us?
head(elev)
##          [,1]
## [1,] 59.60425
## [2,] 58.42156
## [3,] 59.66450
## [4,] 60.00000
## [5,] 60.00000
## [6,] 60.00000

Questions?

Do you see the difference between those two approaches?

  1. Mapping a vector layer on top of a raster layer (i.e. my_map)
  2. Summarizing raster values by vector polygons, then mapping the polygons (elev_map)

Challenge 1: Read in and check out new data

You have another raster dataset in your ./data directory. The file is called nlcd2011_sf.tif.

This is data from the National Land Cover Database (NLCD).

It’s 2011 data that was downloaded from here.

Read that file in as an object called nlcd, and plot it.

Solution

#read in nlcd data
nlcd = raster('./data/nlcd2011_sf.tif')

#plot nlcd
plot(nlcd)

Let’s see what’s in the NLCD data

freq(nlcd)
##       value  count
##  [1,]    11 222187
##  [2,]    21  21713
##  [3,]    22  19966
##  [4,]    23  61919
##  [5,]    24  54480
##  [6,]    31   1150
##  [7,]    41    294
##  [8,]    42   3406
##  [9,]    43   4744
## [10,]    52   7224
## [11,]    71   2109
## [12,]    90    267
## [13,]    95     45

… and a barplot

(Note: The colors in this barplot have no relation to the colors in our maps! Just pay attention to the categories on the x-axis.)

barplot(nlcd)

What do those values mean?

This is a categorical raster. Each cell on the raster holds a discrete (integer) value, coding a particular type of land-cover (rather than a continuous value, like we saw with our elevation data above).

Where do we do to figure out what the codes mean? This should come with the metadarad that ships with your data, or that is provided at the website where you downloaded it.

Here’s the NLCD legend.

Challenge 2: Reproject and crop our NLCD data

Now that we’ve read in our NCLD data, check if we need to reproject it (we want it to be in the same projection as our SFtracts object), and project it if need be.

Then crop it to the extent of our SFtracts object.

Solution

#check projection equality
st_crs(nlcd) == st_crs(SFtracts)
## [1] FALSE
#reproject
nlcd_WGS = projectRaster(nlcd, projectExtent(nlcd, st_crs(SFtracts)$proj4string))

#check projection equality again
st_crs(nlcd_WGS)$epsg == st_crs(SFtracts)$epsg
## [1] TRUE
#crop
nlcd_WGS_crop = crop(nlcd_WGS, SFtracts)

Plot the new raster

plot(nlcd_WGS_crop)

Recovering our plot formatting

Notice that the colors of our original, which conveniently represented the NLCD class colors from their website, are lost after reprojecting and cropping our raster.

Those colors were controlled by information in the original file, which was read into the @legend slot. Here’s the info (with hexadecimal format for color codes, e.g. ‘#00F900’):

nlcd@legend
## An object of class ".RasterLegend"
## Slot "type":
## character(0)
## 
## Slot "values":
## logical(0)
## 
## Slot "color":
## logical(0)
## 
## Slot "names":
## logical(0)
## 
## Slot "colortable":
##   [1] "#000000" "#00F900" "#000000" "#000000" "#000000" "#000000" "#000000"
##   [8] "#000000" "#000000" "#000000" "#000000" "#476BA0" "#D1DDF9" "#000000"
##  [15] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
##  [22] "#DDC9C9" "#D89382" "#ED0000" "#AA0000" "#000000" "#000000" "#000000"
##  [29] "#000000" "#000000" "#000000" "#B2ADA3" "#F9F9F9" "#000000" "#000000"
##  [36] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#68AA63"
##  [43] "#1C6330" "#B5C98E" "#000000" "#000000" "#000000" "#000000" "#000000"
##  [50] "#000000" "#000000" "#A58C30" "#CCBA7C" "#000000" "#000000" "#000000"
##  [57] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
##  [64] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
##  [71] "#000000" "#E2E2C1" "#C9C977" "#99C147" "#77AD93" "#000000" "#000000"
##  [78] "#000000" "#000000" "#000000" "#000000" "#DBD83D" "#AA7028" "#000000"
##  [85] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#BAD8EA"
##  [92] "#B5D3E5" "#B5D3E5" "#B5D3E5" "#B5D3E5" "#70A3BA" "#000000" "#000000"
##  [99] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [106] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [113] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [120] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [127] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [134] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [141] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [148] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [155] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [162] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [169] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [176] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [183] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [190] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [197] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [204] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [211] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [218] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [225] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [232] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [239] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [246] "#000000" "#000000" "#000000" "#000000" "#000000" "#000000" "#000000"
## [253] "#000000" "#000000" "#000000" "#000000"

Recover our plot formatting

What’s the @legend slot in our reproject, cropped object look like?

nlcd_WGS_crop@legend
## An object of class ".RasterLegend"
## Slot "type":
## character(0)
## 
## Slot "values":
## logical(0)
## 
## Slot "color":
## logical(0)
## 
## Slot "names":
## logical(0)
## 
## Slot "colortable":
## logical(0)

Recover our plot formatting

Well that’s a bummer…

Is there a way we could transfer that information over to our reprojected, cropped raster?

Challenge 3: Transferring our @legend info

Try to figure out how to transfer the @legend info from the original raster object to our new object. Then plot the new object to see if it worked.

Solution

Nice! Not necessary… but nice!

nlcd_WGS_crop@legend = nlcd@legend
plot(nlcd_WGS_crop)

Reclassifying rasters

When we’re working with a categorical raster, we’ll often want to reclass our data. We may want to do this because:

  • Our original data has more classifications than we actually need for our analysis.
  • We want to represent the classifications we do have by a different numerical scheme because it somehow makes our analysis more convenient.

Reclass the NLCD

Let’s reclass our NLCD data. First we’ll need to define a reclassification matrix with 3 columns (low, high, to):

?reclassify

Define reclassification matrix

reclass_vec <- c(0, 20, NA, # water will be set to NA (i.e. 'left out' of our analysis)
                20, 21, 1, # we'll treat developed open space as greenspace, based on NLCD description
                21, 30, 0, # developed and hardscape will have 0s
                30, 31, NA, 
                31, Inf, 1) # greensapce will have 1s
reclass_vec
##  [1]   0  20  NA  20  21   1  21  30   0  30  31  NA  31 Inf   1
reclass_m <- matrix(reclass_vec, ncol = 3, byrow = TRUE)
reclass_m
##      [,1] [,2] [,3]
## [1,]    0   20   NA
## [2,]   20   21    1
## [3,]   21   30    0
## [4,]   30   31   NA
## [5,]   31  Inf    1

Reclassify the raster

nlcd_green <- reclassify(nlcd_WGS_crop, reclass_m)

Reclassify the raster

What did we get?

freq(nlcd_green)
##      value  count
## [1,]     0  80545
## [2,]     1  10582
## [3,]    NA 114479

Reclassify the raster

What did we get?

barplot(nlcd_green)

Reclassify the raster

What did we get?

plot(nlcd_green)

Challenge 4: Extract reclassed NLCD data to our tract polygons

Just like we did earlier with our elevation data, let’s extract our reclassed NLCD data to our census-tract polygons.

Solution

#extract the mean nlcd_simple values to tract polygons
greenspace = extract(nlcd_green, SFtracts, fun=mean)

What did we get?

greenspace
##               [,1]
##   [1,] 0.000000000
##   [2,] 0.000000000
##   [3,]          NA
##   [4,] 0.000000000
##   [5,] 0.000000000
##   [6,] 0.000000000
##   [7,] 0.000000000
##   [8,] 0.000000000
##   [9,] 0.000000000
##  [10,] 0.000000000
##  [11,] 0.000000000
##  [12,] 0.003773585
##  [13,] 0.055555556
##  [14,] 0.000000000
##  [15,] 0.000000000
##  [16,] 0.000000000
##  [17,] 0.000000000
##  [18,] 0.000000000
##  [19,] 0.000000000
##  [20,] 0.000000000
##  [21,] 0.000000000
##  [22,] 0.000000000
##  [23,] 0.000000000
##  [24,] 0.002762431
##  [25,] 0.000000000
##  [26,] 0.000000000
##  [27,] 0.017482517
##  [28,] 0.002159827
##  [29,] 0.000000000
##  [30,] 0.000000000
##  [31,] 0.000000000
##  [32,] 0.000000000
##  [33,] 0.001628664
##  [34,] 0.066889632
##  [35,]          NA
##  [36,] 0.000000000
##  [37,] 0.006944444
##  [38,] 0.008605852
##  [39,] 0.008163265
##  [40,] 0.007407407
##  [41,] 0.000000000
##  [42,] 0.000000000
##  [43,] 0.050193050
##  [44,] 0.000000000
##  [45,] 0.000000000
##  [46,] 0.000000000
##  [47,] 0.000000000
##  [48,] 0.000000000
##  [49,] 0.015761821
##  [50,]          NA
##  [51,] 0.010810811
##  [52,] 0.000000000
##  [53,] 0.000000000
##  [54,] 0.000000000
##  [55,] 0.000000000
##  [56,] 0.000000000
##  [57,] 0.000000000
##  [58,] 0.000000000
##  [59,] 0.000000000
##  [60,] 0.000000000
##  [61,] 0.000000000
##  [62,] 0.018867925
##  [63,]          NA
##  [64,] 0.000000000
##  [65,] 0.000000000
##  [66,] 0.000000000
##  [67,]          NA
##  [68,] 0.000000000
##  [69,] 0.042471042
##  [70,] 0.000000000
##  [71,] 0.000000000
##  [72,] 0.000000000
##  [73,] 0.000000000
##  [74,] 0.013953488
##  [75,] 0.016129032
##  [76,] 0.033582090
##  [77,] 0.000000000
##  [78,] 0.043478261
##  [79,] 0.000000000
##  [80,] 0.064220183
##  [81,] 0.033254157
##  [82,] 0.000000000
##  [83,] 0.000000000
##  [84,] 0.008968610
##  [85,]          NA
##  [86,] 0.000000000
##  [87,] 0.000000000
##  [88,] 0.000000000
##  [89,] 0.000000000
##  [90,] 0.000000000
##  [91,]          NA
##  [92,]          NA
##  [93,] 0.000000000
##  [94,] 0.000000000
##  [95,] 0.032624113
##  [96,] 0.000000000
##  [97,] 0.000000000
##  [98,] 0.000000000
##  [99,]          NA
## [100,]          NA
## [101,]          NA
## [102,]          NA
## [103,] 0.000000000
## [104,]          NA
## [105,] 0.000000000
## [106,] 0.000000000
## [107,] 0.000000000
## [108,] 0.000000000
## [109,]          NA
## [110,] 0.000000000
## [111,] 0.058035714
## [112,]          NA
## [113,] 0.000000000
## [114,] 0.000000000
## [115,]          NA
## [116,] 0.000000000
## [117,] 0.012755102
## [118,] 0.000000000
## [119,] 0.004056795
## [120,]          NA
## [121,] 0.000000000
## [122,] 0.043209877
## [123,] 0.024258760
## [124,] 0.029562982
## [125,] 0.005555556
## [126,] 0.007722008
## [127,] 0.005504587
## [128,] 0.000000000
## [129,] 0.000000000
## [130,]          NA
## [131,] 0.005444646
## [132,] 0.031746032
## [133,] 0.002969562
## [134,] 0.000000000
## [135,] 0.003992016
## [136,] 0.000000000
## [137,] 0.000000000
## [138,] 0.000000000
## [139,]          NA
## [140,] 0.000000000
## [141,] 0.000000000
## [142,] 0.000000000
## [143,] 0.002906977
## [144,]          NA
## [145,]          NA
## [146,]          NA
## [147,] 0.000000000
## [148,]          NA
## [149,]          NA
## [150,] 0.000000000
## [151,] 0.000000000
## [152,] 0.000000000
## [153,] 0.000000000
## [154,] 0.000000000
## [155,] 0.000000000
## [156,] 0.000000000
## [157,] 0.000000000
## [158,] 0.000000000
## [159,] 0.000000000
## [160,] 0.000000000
## [161,] 0.000000000
## [162,]          NA
## [163,] 0.000000000
## [164,] 0.000000000
## [165,] 0.000000000
## [166,]          NA
## [167,]          NA
## [168,] 0.000000000
## [169,] 0.000000000
## [170,] 0.000000000
## [171,] 0.018335684
## [172,]          NA
## [173,] 0.001703578
## [174,] 0.000000000
## [175,] 0.000000000
## [176,]          NA
## [177,]          NA
## [178,] 0.000000000
## [179,]          NA
## [180,] 0.000000000
## [181,] 0.000000000
## [182,]          NA
## [183,]          NA
## [184,] 0.000000000
## [185,] 0.000000000
## [186,] 0.000000000
## [187,] 0.000000000
## [188,] 0.000000000
## [189,]          NA
## [190,]          NA
## [191,] 0.006535948
## [192,] 0.000000000
## [193,]          NA
## [194,]          NA
## [195,]          NA

Why?

What’s with all the NAs?

Remember, we set all water cells to NA, to ignore them in our analysis.

Challenge 5: How do we get extract to ignore our NAs?

Try to run the same command again, but telling the extract function to ignore NAs.

Solution

The na.rm argument will do this for us. See how the docs indicate that it is set to FALSE by default?

?raster::extract

Good to know! Also good to know that this is a common argument across a variety of R operations.

Solution

#extract the mean nlcd_simple values to tract polygons,
#this time setting na.rm to TRUE
greenspace = extract(nlcd_green, SFtracts, fun=mean, na.rm = T)

#and add to our SFtracts dataframe (which we can do because order is preserved)
SFtracts$prop_greenspace = greenspace

Get the mean home values in each tract

Pulling code from the end of Part II of this workshop, let’s aggregate our homes data to the tract level too.

#aggregate totvalue to SFtracts
SFtracts_w_mean_val = aggregate(x = SFhomes15_sf['totvalue'],
                                by = SFtracts,
                                FUN = mean)
## although coordinates are longitude/latitude, st_intersects assumes that they are planar
#and add the totvalue column to our SFtracts dataframe
SFtracts$mean_totvalue = SFtracts_w_mean_val$totvalue

Get the mean home values in each tract

qtm(SFtracts_w_mean_val, fill = 'totvalue')

Predicting home values

Do mean elevation and proportion greenspace predict mean home values?

(Note: This is not a statistically valid model! Just a stand-in for downstream analysis.)

mod = lm(mean_totvalue ~ mean_elev + prop_greenspace, data = SFtracts)
summary(mod)
## 
## Call:
## lm(formula = mean_totvalue ~ mean_elev + prop_greenspace, data = SFtracts)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -713126 -303774    9710  246766 1757701 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     1167067.1    61177.3  19.077   <2e-16 ***
## mean_elev          1343.2      832.9   1.613    0.109    
## prop_greenspace -351753.5   369815.0  -0.951    0.343    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 377600 on 184 degrees of freedom
##   (8 observations deleted due to missingness)
## Multiple R-squared:  0.01682,    Adjusted R-squared:  0.006136 
## F-statistic: 1.574 on 2 and 184 DF,  p-value: 0.21

Predicting home values

Not at the census-tract level. But that’s kind of coarse…

What if we want to do the analysis at the property level?

Here’s a workflow that puts together a bunch of what we’ve learned over Parts I to III of the workshop!

#Take a random subset of our 2015 homes, to save on computer time
SFhomes15_sample = SFhomes15_sf[sample(seq(nrow(SFhomes15_sf)),
                                replace = FALSE, size = 2000), ]

Predicting home values

Now let’s reproject all our data to a UTM projection, so that we units of meters rather than decimal degrees.

#reproject
SFhomes15_utm <- st_transform(SFhomes15_sample, 26910)
DEM_utm = projectRaster(DEM,
                        projectExtent(DEM,
                                      st_crs(SFhomes15_utm)$proj4string))
nlcd_green_utm = projectRaster(nlcd_green,
                               projectExtent(nlcd_green,
                                             st_crs(SFhomes15_utm)$proj4string))

#check projections
st_crs(SFhomes15_utm) == st_crs(DEM_utm)
## [1] FALSE
st_crs(SFhomes15_utm) == st_crs(nlcd_green_utm)
## [1] FALSE

Predicting home values

Now let’s buffer all our homes with a 100-meter buffer, then sum the greenspace within those buffers.

#create buffer
SFhomes15_utm_buff = st_buffer(SFhomes15_utm, dist = 100)

#sum the greenspace within the buffers 
#NOTE: This will take a couple minutes to run...
greenspace_homes = extract(nlcd_green_utm, SFhomes15_utm_buff, fun = mean, na.rm = T)

#add that as a column in our SFhomes15_utm dataframe
SFhomes15_utm$greenspace = greenspace_homes

Predicting home values

And now let’s extract the elevation at each home.

#extract the elevation to the homes
#NOTE: no need for fun or na.rm arguments here, because the homes
#and points, not polygons, so only a single cell will extract to each
elev_homes = extract(DEM_utm, SFhomes15_utm)

#add that as a column in our SFhomes15_utm dataframe too
SFhomes15_utm$elev = elev_homes

Predicting home values

Now, how about that regression model?

mod = lm(totvalue ~ elev + greenspace, data = SFhomes15_utm)

Predicting home values

Mehhh… Some signal for elevation, but a very low \(R^{2}\).

But again, this is just a stand-in for downstream analysis.

summary(mod)
## 
## Call:
## lm(formula = totvalue ~ elev + greenspace, data = SFhomes15_utm)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1155859  -412030  -102095   303608  1750949 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1241715.3    22753.6  54.572   <2e-16 ***
## elev            295.5      312.1   0.947    0.344    
## greenspace   101606.9   285316.2   0.356    0.722    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 561200 on 1997 degrees of freedom
## Multiple R-squared:  0.0005766,  Adjusted R-squared:  -0.0004243 
## F-statistic: 0.5761 on 2 and 1997 DF,  p-value: 0.5622

Questions?

Section 3: RasterStacks and RasterBricks

RasterStacks

What about working with multiple rasters?

Fog data

Data on summertime coastal fog in CA (a.k.a. Karl)

#(from http://climate.calcommons.org/dataset/monthly-summertime-fog)
#(units are in average hours per day)
karl_files = unique(gsub('.aux.xml', '', list.files('./data/CalMnYr')))
karl_files = karl_files[grep('flcc', karl_files)]

# Take  a look
karl_files
##  [1] "flcc1999aug" "flcc1999jul" "flcc1999jun" "flcc1999sep" "flcc2000aug"
##  [6] "flcc2000jul" "flcc2000jun" "flcc2000sep" "flcc2001jul" "flcc2001jun"
## [11] "flcc2001sep" "flcc2002aug" "flcc2002jul" "flcc2002jun" "flcc2002sep"
## [16] "flcc2003aug" "flcc2003jul" "flcc2003jun" "flcc2003sep" "flcc2004aug"
## [21] "flcc2004jul" "flcc2004jun" "flcc2004sep" "flcc2005aug" "flcc2005jul"
## [26] "flcc2005jun" "flcc2005sep" "flcc2006aug" "flcc2006jul" "flcc2006sep"
## [31] "flcc2007aug" "flcc2007jul" "flcc2007jun" "flcc2007sep" "flcc2008aug"
## [36] "flcc2008jul" "flcc2008jun" "flcc2008sep" "flcc2009aug" "flcc2009jul"
## [41] "flcc2009jun" "flcc2009sep"

RasterStack

Read all of the KARL files into one RasterStack object

karl <- stack(paste0('./data/CalMnYr/', karl_files))

# look at what we made!
karl
## class      : RasterStack 
## dimensions : 256, 250, 64000, 42  (nrow, ncol, ncell, nlayers)
## resolution : 0.0314827, 0.0314827  (x, y)
## extent     : -128.0284, -120.1578, 33.96418, 42.02375  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=NAD83 +no_defs +ellps=GRS80 +towgs84=0,0,0 
## names      : flcc1999aug, flcc1999jul, flcc1999jun, flcc1999sep, flcc2000aug, flcc2000jul, flcc2000jun, flcc2000sep, flcc2001jul, flcc2001jun, flcc2001sep, flcc2002aug, flcc2002jul, flcc2002jun, flcc2002sep, ... 
## min values :        1.85,        0.56,        1.69,        0.26,        0.78,        1.05,        1.23,        1.74,        1.29,        1.32,        1.23,        0.30,        1.20,        0.13,        0.86, ... 
## max values :       15.72,       18.56,       17.84,       18.26,       14.84,       18.21,       17.37,       12.18,       20.44,       16.50,       15.20,       17.65,       16.85,       14.87,       14.87, ...

A RasterStack object - literally what it sounds like!

Plot the Stack

#plot a few
plot(karl[[7:9]])

CRS

What’s the projection of the RasterStack?

#what's the projection?
st_crs(karl)
## Coordinate Reference System:
##   EPSG: 4269 
##   proj4string: "+proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs"

CRS Transformation

Let’s reproject this

karl_WGS = projectRaster(karl, projectExtent(karl, st_crs(SFtracts)$proj4string))

# check resultant CRS
st_crs(karl_WGS)$epsg == st_crs(SFtracts)$epsg
## [1] TRUE

What did we get?

What type of spatial object did that give us?

karl_WGS
## class      : RasterBrick 
## dimensions : 256, 250, 64000, 42  (nrow, ncol, ncell, nlayers)
## resolution : 0.0314827, 0.0314827  (x, y)
## extent     : -128.0284, -120.1578, 33.96418, 42.02375  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=NAD83 +no_defs +ellps=GRS80 +towgs84=0,0,0 
## source     : /tmp/RtmpgUUT8U/raster/r_tmp_2020-02-05_141046_8950_92310.grd 
## names      : flcc1999aug, flcc1999jul, flcc1999jun, flcc1999sep, flcc2000aug, flcc2000jul, flcc2000jun, flcc2000sep, flcc2001jul, flcc2001jun, flcc2001sep, flcc2002aug, flcc2002jul, flcc2002jun, flcc2002sep, ... 
## min values :        1.85,        0.56,        1.69,        0.26,        0.78,        1.05,        1.23,        1.74,        1.29,        1.32,        1.23,        0.30,        1.20,        0.13,        0.86, ... 
## max values :       15.72,       18.56,       17.84,       18.26,       14.84,       18.21,       17.37,       12.18,       20.44,       16.50,       15.20,       17.65,       16.85,       14.87,       14.87, ...

RasterBrick

A RasterBrick. What does that mean?

# See the documentation!
?raster::brick

Crop the Brick

Crop it to the extent of our area of interest - SF

# Crop it to SFtracts
karl_WGS_crop = crop(karl_WGS, SFtracts)

#Note that R vectorized that operation across our entire RasterBrick, the same way that it vectorizes many operations, e.g. 3<4 vs 3< seq(4)

Plot it

# now let's make our same plot again
par(mfrow = c(1,2))
plot(karl_WGS[[7]])
plot(st_geometry(SFtracts), add = T, reset=F, key.pos = NULL, col = NA)
plot(karl_WGS_crop[[7]])
plot(st_geometry(SFtracts), add = T, reset = F, key.pos = NULL, col = NA)

Mean Fog

Let’s mean the karl values across the RasterBrick

# Mean values
mean_karl_WGS_crop = mean(karl_WGS_crop)

What did that give us?

mean_karl_WGS_crop
## class      : RasterLayer 
## dimensions : 5, 6, 30  (nrow, ncol, ncell)
## resolution : 0.0314827, 0.0314827  (x, y)
## extent     : -122.519, -122.3301, 37.71062, 37.86803  (xmin, xmax, ymin, ymax)
## crs        : +proj=longlat +datum=NAD83 +no_defs +ellps=GRS80 +towgs84=0,0,0 
## source     : memory
## names      : layer 
## values     : 4.71, 12.3719  (min, max)

RasterBrick to Raster

When we computed the mean of a RasterBrick we got back a RasterLayer object! That makes sense, because we took cellwise means across all Layers in our Brick.

This is called raster algebra

Plot it

plot(mean_karl_WGS_crop)
plot(st_geometry(SFtracts), add = T, col = NA)

BUT

Not all common operations successfully run as raster algebra

# This won't work
sd_karl_WGS_crop = sd(karl_WGS_crop)

Let’s try this instead

sd_karl_WGS_crop = calc(karl_WGS_crop, sd)

Plot it

#plot that too
par(mfrow = c(1,2))
plot(mean_karl_WGS_crop, main="mean summer fog hours")
plot(st_geometry(SFtracts), add = T, reset=F, key.pos=NULL, col = NA)
plot(sd_karl_WGS_crop, main="sd summer fog hours")
plot(st_geometry(SFtracts), add = T, reset=F, key.pos=NULL, col = NA)

Thoughts…

Looks like the foggiest neighborhoods also have the highest variation in fog, but some less foggy neighborhoods on the east side of the city (e.g. The Inner Mission, Bayview) also vary quite a bit

Extract Mean Values

Extract fog values to our tracts

SFtracts$mean_karl = extract(mean_karl_WGS_crop, SFtracts, mean)

Explore Spatial Relationships

Maybe fogginess is a function of elevation? That would make sense, right?

# Linear regression model
mod = lm(mean_karl ~ mean_elev, data = SFtracts)

View results

summary(mod)
## 
## Call:
## lm(formula = mean_karl ~ mean_elev, data = SFtracts)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0659 -1.2745 -0.3786  0.9346  4.2184 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 7.830075   0.242622  32.273  < 2e-16 ***
## mean_elev   0.009123   0.003334   2.736  0.00685 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.491 on 180 degrees of freedom
##   (13 observations deleted due to missingness)
## Multiple R-squared:  0.03992,    Adjusted R-squared:  0.03459 
## F-statistic: 7.485 on 1 and 180 DF,  p-value: 0.006845

Comments

Neat!

Census-tract mean elevation has a significant, positive effect on mean fogginess (with each meter increase in elevation causing on average a .011 hour, or about 39-second increase in time spent in fog on an average summer day.

Though this barely explains about 4% of the variance in our data!

Of course, again, these are not statistically valid models! Just analytical stand-ins.

Questions?